Personally I'm not that comfortable trying to get with girls who have boyfriends. However if they genuinely aren't enjoying or satisfied with the boyfriend they have then I see no problem with rescuing a 'damsel in distress' after all this is the gentlemanly thing to do. Most guys when they find out a girl has a boyfriend will eject, they take the statment 'I have a boyfriend' at face value and assume it's game over.

I guess the thing to do is ask questions of this relationship, elicit emotions from her regarding her relationship and then from there calibrate how strongly she feels about the relationship. Get her to talk about her boyfriend, listen to how she talks about him, is this in a positive light or a negative light??

Never ever disrespect or say anything negative about the boyfriend or judge him in anyway. If you do this, regardless even if she is unhappy in her relationship with the boyfriend she will most likely back him up and stick up for him making you look like a total dick. Talk postively about the boyfriend whenever you can and if she starts to say something like 'Yeah he's alright, but he does this, this and this which annoys me'. Then you have more of a picture about her current relationship and can proceed with caution
instead of turning and bailing whenever you see a percieved red light.