"Me" is not a dirty word

Or an implied “are”. If it’s “Bob is older than we are”, “we” is a subject and so is “I”, so, “Bob is older than Bill and I [are].”

I think I love you. It’s nice to know I’m not screaming alone.

I thought I had a pretty good feel for English, but “he’s older than me” just doesn’t bother me. I’d probably never say “Bob is older than I” without having to think twice.
As for “Bob and I’s friend”, I think fachvirwirrt’s suggestion of making the possessive parallel (Bob’s and my friend) is the most natural.

I find myself saying “Bob is older than I am” so it doesn’t sound stilted but is also correct.