This is hard for me as well, because I really don't understand the lines between platonic friend and girlfriend. I've not had romantic feelings for someone. I've deeply cared for a lot of people, wanted to disclose everything I could to them and hope they felt the same way toward me, but never a romantic feeling of wanting to commit and spend the rest of my life with them. That kinda makes it hard to connect with a lot of people, and doubly hard for people who I have an attraction to.
I did have a girlfriend, and the reason it worked was because we both had similar feelings and chose to leave everything open. Cheating wasn't really in our vocabulary, unless it was done with some malicious intent. Indeed we became pretty comfortable talking to each other about people we found interesting or attractive. There was never a fear of being replaced, and I think that played a large part in making it work.
A couple years ago she moved 12 hours away for reasons that I won't go into now, but we still are very close. She has had another boyfriend since, and has told me about him. We even talked about some of the weird qwerky stuff her and I used to do, and I would ask if he had taken to any of that. We had this conversation as though we were chilling at McDonalds. She even asked if I wanted to meet him, again like we were inviting a family friend. I initially wanted to, until I learned that him and I disagreed on a lot of things. That was pretty much the only reason though. The conversation felt so weird, but I wouldn't have wanted it any other way, and until that point I only imagined such things in a fantasy world. To this day I don't know why she shares my way of looking at our relationship, but it's something she's admitted to struggling with after she moved. A lot of people just don't get tthat way of thinking it seems. i'll probably not understand it, but I accept the fact that I'm the odd one out.
Meeting a girl with a boyfriend, when you don't know either of them too well, can be hard especially if you find the girl attractive. Just the other day I saw a girl friend who wanted to introduce me to her boyfriend. Even though her and I are platonic, we do have some close contact (handholding, head pats, sometimes a hug when we leave), and so I was afraid she wouldn't let this continue when her boyfriend was around. She did, but I felt so awkward. Her boyfriend was quiet, so I had no clue what he thought of our antics. He seemed cool, but too quiet to tell what was on his mind. I don't know how traditional her views are on commitment and relationships and the like, and that's a really awkward position to be in, and an even more awkward conversation to have. I'm attracted to her, but not as much as I was to the girl I talked about earlier. So I really have no desire to pull her away from her boyfriend. All the same I am attracted to her enough to seek contact more often than I do most people. Now if she, against all my expectations, told me she wanted to start a relationship with me, I'd not be opposed to it but I really have no idea how it would go. I don't expect that to happen though, nor am I prepared for it and so I won't be the one to bring it up. I'd be better off with someone who I've not yet met.
The way I see it, there's no real right way to handle such a situation because people and their views are so wide ranging and impossible to predict. If you approach a girl and she has a boyfriend, I wouldn't be afraid. Maybe a little cautious if you don't know what to expect, but if you're afraid or nervous, things won't ever go right. The best thing you can do is try to scope the situation adequately before deciding how you feel. If you feel attraction, either stay away or just be really careful.. I'm not sure if you and I have similar struggles, but I hope maybe this has helped a little. It's not much, but it's all I got.