Don't try and wheel a girl with a boyfriend unless their relationship is absolutely ending soon, its pretty fucking low. I'll admit I have hooked up with taken girls before but its been random one night drunken encounters. I would personally never go after a chick WITH a bf tbh. Even the times I did, I felt pretty fucking bad about.
I've been in a similar situation though, where a girl I studied/hung out with a lot had a bf but I liked her. I became her friend, they eventually broke up, and we eventually did hook up. Nothing came of it but we are still friends and im not "that asshole" that messed up a relationship. So my advice in this situation is just be a friend for now but stay flirty. If she DOES make the first move...well then its up to you :p. Also I don't know what kind of guy this is, but if someone went after my current gf and I saw him out at the bar/club one night....shit would not end pretty to say the least haha.
Now on to the TA...
I actually TA university biology class
. I'm only 22 and most of my students are 18-21 so we are almost the same age and I definitely hang out with people their age. I guess its different for men bc I would gladly bang half of the 1st years in my class rofl (I blame male hormones). I got friendly with a few, as in, they would stay after and chat up a storm with me. I do consider myself a good looking guy with a sense of humour so the girls always hit on me. I got funny pictures and notes written on assignments sometimes and even my TA evaluations were hilarious with some of the girl ones straight out admitting I was cute etc. Personally, I thought the attention was awesome, and if any of them legitimately asked me out I probably would have after my TAship was done. You can maybe start there, bc in my experience the ones that stayed after and talked stood out. Some just needed actual help but some just chatted about random stuff. Those were the ones where I knew their names off my by heart. Then maybe if you have stuff to hand in, that ONLY goes to her (no other TAs/instructors,profs) draw funny stuff on it maybe. Nothing too forward but I definitely appreciated some humour while mundanely marking 100 assignments.
TA's at the end of the day are just like you, just maybe 1 or 2 years ahead in education. The only risk is whether or not she thinks its morally alright to date a student, at least while she is your TA.
I had an encounter where I ran into a student out at a bar. She was obviously drunk but she blatantly hit on me, bought me drinks and danced. We did make out briefly but I was pretty sober plus really new to TA'ing and didnt want to get in shit. She invited me to her place and I turned it down (yeah I know, WTF?!). So even though I consider myself to have low morals when it comes to women, I wouldnt want to hook up with a student WHILE I am their TA. Plus, girls are typically batshit insane and I'm scared one of them does blackmail me for higher marks or some shit. Or rats me out once I stop giving a fuck. Seriously.
At the end of the day, keep hitting on your TA, be funny, playful etc. Maybe near the end of the semester lean towards hanging out outside of class because then if anything transpires she wont be your TA for long. I actually do run into old students that were friendly here and there, boy or girl, and if I got along with them in class we typically chat a bit and I wouldnt mind hanging out with them outside of class.
Now if you go ahead and ask her out now, I'd say you are still safe anyways. Shes just a young student herself, not like asking out a high school teacher or professor lolol so the risk is low...unless you get turned down then going to class gets awkward haha.