Walk out the door, shift my eyes from side to side, whistle quietly and try to look inconspicuous.
Reach into the piss and shit water, pick up the soggy roll, toss it in the trash, wash your hands. It is excrement, people; not plutonium. Nobody ever died from touching their own shit.
Gazillions of people who die every year of fecal borne illness would like to chat with you about that. 'Cept they can’t, being dead and all… 
That’s because they didn’t wash their hands.
At this point you might as well throw the jacket you used to inadvertently knock the roll into the toilet and try to flush it.
Isn’t the problem more a matter of coming in contact with other people’s feces?
Anyway, I think those nifty waxed paper bags they leave in the ladies’ room stalls would come in handy if I had to fish out a roll of TP from the toliet.
Walk away.
“Need answer quick”? 
I’d use my dick. Wouldn’t most guys?
mangetout, this is a circumstance that justifies your collection of single gloves.
Yeah, but I’d rather put my hand in shit than in most of the discarded gloves I see, especially the latex ones.
Fish it out, toss it in the trash, and wash my hands.
As the father of two kids (and primary household mess-cleaner-upper) I long ago lost any fastidiousness about dealing with shit.
WWJSD
What Would James Sunderland Do?
Stick his whole arm in, without even rolling up his sleeves, to fish that Important Item out.
This is the worst RPG ever.
Probably laugh a little, wait till the rooms clears out and go back to the office and tell my buddy that some piece of shit threw a whole roll of tp in the shitter and just left it there.
This is what most men would do contrary to what most are claiming in this thread.
Win 
I’m in the camp that says take responsibility, fish it out (hopefully by still being able to grab a dry end), chuck it in the trash and wash hands. It’s kind of a no brainer, really. It sucks, but you have to be an adult, and it’s really only a few seconds of discomfort.
This is what I think, but I’ve seen threads here on the SDMB where people talk about using wads of tissue just to touch a door handle that other people might have soiled. I wonder what those folks would do in this situation. Maybe they’re in the ‘walk away’ camp and have just refrained from posting in this thread.
You spend 10-15 seconds analyzing the situation and come to the conclusion that there is no outcome that will save your dignity.
The best possible outcome is to cause panic and confusion.
Close the toilet lid - you’re not going in there - it’s a lost cause. Get the remaining toilet rolls from the shelf and stack them up on the toilet seat in a pyramid formation, or the closest approximation thereto.
Tear off a three foot length from one roll. If you have a pen that’s great, but if not use your finger and the toilet blue to write: “Death to all infidels!” drape that over the stall door so that people from outside can see it.
Set the toilet roll pyramid on fire from the base.
Get down on your hands and knees and crawl out to an adjoining stall.
Make your escape and if you are seen by anyone yell “terrorist attack in the bathroom!” as you dash towards the elevators. If you are not seen, just walk back to your office and let someone else discover the bathroom horror.
It’s the only way to be sure.
Edit: I joke, of course, I’ve had shit on my hands before. It washes off. Fish the roll out, try not to get it all splashed over yourself and wrap it up in more toilet paper, dispose of it in a bin, and wash your hands and forearms down with soap.
Now that would be an awesome text-based RPG.