I've gotten pretty good at starting and holding conversations with girls. In other words, I pretty good at becoming friends with female strangers (not what I'm going for).

However, I don't know how to move the conversation to something related to relationships/sex. This is because I don't go to bars, so the girls I approach are coworkers, classmates, friend of friends, etc. There is higher risk than bars/clubs.

For example, today I went to a company event and talked with a girl for several hours. It didn't feel right to ask her about whether she had a boyfriend because my coworkers were all around us (often within earshot). Eventually, our conversation moved towards travel and she mentioned that she recently went somewhere with her boyfriend. I expected this, so I didn't mind too much, but it would've been nice to start talking about relationships sooner so I can find out sooner.

How do you move a conversation from a normal conversation to one involving relationships/sex?