That’s just the thing, though – we really didn’t talk about anything but lost IDs. I brought up actuarial tables because I know – from her ID – that she works for an insurance company.
I suppose my best hope is to run into her on the street. And that seems unlikely. There are people in my own building that I’ve hoped to run into “accidently”, and it can take months or even years for that to happen, if it does at all.
Eh, just call her & tell her the truth. Worst case scenario - she’ll think you’re a nut & hang up on you or something. And you’ll be better off than you are now, cause at least you’ll know you have no chance 
Best case scenario - she’ll agree to meet you for dinner or something, then - well, then who knows.
Call her up & say something like “Hey, I’m the guy that returned your ID the other day. I know it’s kinda weird, but I enjoyed meeting you & wonder if you’d like to grab a bite to eat sometime?”
You sweet talker, you. With that sort of scintillating conversation running through her head, she’s probably desperate for another chance, so she can get your thoughts on the life expectancy of a non-smoker with a family history of depression.
The more I think about it, your best chance to ask her out was probably when you met her. That moment may be lost, now. Sometimes, I think, the spontaneous meetings are more successful then the planned encounters for securing a first date with a stranger.
Here’s the scenario, in full, as far as I can remember it:
I found the ID on the street, about a block south of where I live, in the morning.
Around 10am, I called the insurance company and asked for her by name. When she answered, I didn’t identify myself, I just asked if she’d lost an ID. She sounded delighted that I’d called. She asked if I was in the building, and if I’d found it in the lobby, and could she come get it right now. I told her that I was, in fact, on the other side of town. I asked where she lived. She told me not only the town, but the street, and even her address (sans apartment number). I told her my address. (It’s maybe half a block south of her. Putting this together, she’s about a block north of where she lost her badge.)
I suggested returning it to her after work, and gave her my phone number. She said she’d call when she got home, at 5:30. I told her that I wouldn’t be home until maybe 6:30. She gave me her cell. She thanked me a few dozen times, then hung up.
I arrived home at 6:15. She had left a message at 6:00, saying she was home, and once again gave me her cell number.
I changed my clothes and called. Instead of asking who it was, she gave a hearty “Hi Todd!” (Gotta love caller ID.) I told her “Walk to my apartment, and I’ll walk to yours, and we’ll meet in the middle.” She agreed.
Minutes later, I was on the sidewalk, walking towards someone resembling her picture. At first she looked a little suspicious at the guy smiling at her, then caught on and took the ID from me. She showed me her temp ID still clipped to her belt. She asked me where I’d found the original, and I said “Over there, on the median where the flowers are.” Chit chat and thanks for maybe a minute or two. It was all warm and smiley. She thanked me for walking to meet her halfway. I commented that it was really not far, referencing my building, which was spitting distance away. She laughed. We said goodbye.
That’s pretty much it.
How do I love thee? Let me itemize the deductable.
To set it straight, I brought up actuarial tables here, not with her.
If I were a woman, there’s no way in hell I wouldn’t get a creepy vibe out of this. She’d probably think, Some guy “finds” my work ID and now wants to ask me out? How did I lose my ID, anyway? Did I really drop it absent-mindedly or did he snatch it while I was inattentive and is now using a perfectly good excuse to stalk me?
That thought crossed my mind.
I think my best move is to introduce her number to Mr. Trash Barrel. If, by some miracle, she wants to call me, she has my number. I expect to become God’s Own Orthodontist before then, though.
Good call, tdn. I’m about that age, and I think it’s pretty skeevey when I get hit on by older guys who know nothing about me except how I look. It’s just way, way too obvious.
As another 20-something female, I agree that you’re probably better off leaving this alone so she has a positive memory of what a good guy you were to return it instead of trying to call and most likely causing her to become suspicious and creeped out.
But IF you really feel that it would be better to take the big risk instead of wonderign “what if?”, I agree with the idea of just asking her out instead of trying to be “friends”.
Most 20-something women get hit on by older guys quite often. I once took a 40-something man’s offer to be “friends” at face value when I was about 19. I quickly realized how naive I was to assume that he wouldn’t be interested in me in That Way just because his daughter was my age. 
But, hey, there is always the small chance that she is one of those girls who happens to like older guys, so if you can handle the likelihood of getting shot down then I don’t think it would be that bad to call just once to ask her out.
Chiming in with the others who say that 22-year-old women are usually not interested in hanging out with men old enough to be their fathers. She sounds friendly, not to mention glad that you’ve found her ID, but I’ve found that what I consider to be normal friendliness is often interpreted by men as flirtiness or interest.
You could try calling and asking her out, but if I that kind of call, my first thought would probably be “Oh, shit, I can’t believe I was dumb enough to give him my address!”
My first thought might be a little less charitable. It might be "Oh, that old guy didn’t think I was interested in him, did he? Oh, dear. " 
All that being said, the way the conversation went down, I suppose you could hint just one time. Be prepared for not nice thoughts, be prepared for a big NO! And please, please, take NO for an answer and dont’ keep hounding her and “accidentally” running into her.
I wouldn’t do that, and I’m pretty sure that if I do run into her again, it will truly be accidental.
The thing is, while a romantic relationship would be cool, I’d honestly be up for a platonic relationship. That’s really the extent of my intentions. Honest! But it looks like there’s no way of making that happen without making it look like something far different. How ironic.
I like lavenderviolet’s idea. Let her last impression of me be a positive one.
How come all of the things that work so very, very well in romantic comedies will get you slapped with a restraining order and domestic disturbance citation in real life? Hell, do chicks in real life even like Peter Gabriel? Regardless, Lloyd Dobler is still a more rightous dude than that self-satisfied toady Ferris Bueller. I hate that guy.
Anyway, I don’t have any brilliant advice for the o.p. except to stop deluding himself about his intentions, to wit “…I’d like to be friends with her. I could see us going on walks together, or to movies, or whatever. Friend stuff.” Dude, if you wanted to be friends, you wouldn’t be waffling about this; you’d just call her up and invite her to shoot some pool, or whatever. You’re interested in her in a very real and non-not-romantic sense, and you should either step up to the plate and swing–whether you strike out or knock it out of the park–or find another team to play with. Me, I’d probably forget about it, pour another glass of Black Bush, and finish off that Highsmith novel I started reading last night, but if you decide to go for it, good luck on you.
Stranger
And Ferris was so not a ladies’ man in that movie. He didn’t even get any girl; he started the movie with the girl, and all he accomplished during the movie was that his best friend got to see her naked by pretending to be catatonic while she changed into her bathing suit.
When a guy calling himself “Stranger on a Train” gives you the advice to back off the girl you barely know, it’s time to take it seriously. 
Now, this I don’t understand. She’s not going to have much of an impression of you at all in about a week. In a year, she’ll have forgotten you exist. And you’ll never see her again.
Now assume you call her & she gets the ‘creepy stalker vibe’ from you - the same thing is true! And you’ll still never see her again.
I don’t understand your hesitation. If you’re already resigned to never seeing her again, what do you have to lose?
I think the “no chance” crowd is probably right, unfortunately. If you think it might be skeevy, it probably is.
I think this is the best way to go. Then if you do accidentally run into her you two could have another chit-chat about whatever and then you could get another feel about her and the situation and whether you want to try to be friends with her.
And if at that run-in you get a vibe that she might be inclined to be friends you should definitely call her up a day or two later for a walk or whatever. She still might say no of course but at least you can be confident in your attempt.
I think she’s just a friendly outgoing person, nothing in what you wrote would indicate that she was into you. She was motiviated to keep in touch to get her badge back.
OTOH, maybe she lost her badge on purpose just to meet guys! That sneaky little tramp!
Trust me, this morning I was examining the ground closely while on my way to work.
Tahssa, I like your idea, but it has one fatal flaw. If I run into her again in, say, a year, should I really still have her phone number?
Almost forty chiming in.
I’d call her and ask her if she’d seen YOUR ID on her way to work?