I've been to 2-3 mixers for singles in my city. It's usually a bar packed with people standing around and talking. If a woman is currently talking to a single man 1:1, what's an appropriate way for me to join the conversation so I can introduce myself to her?

I'm able to approach groups and join in on conversations, specially if the group is mixed gender.

However, I notice that most people are talking one on one. I've waited around going to see an opening when the guy leaves or she walks away, but they keep talking. When I leave to get a drink or go around the room and return, she's taking to a different guy. Many times in the exact spot she was standing in before. And this seems applicable for most people, not me targeting a few attractive women at an event.

Just intruding into a conversation between two people with a "hi" seems rude? But other men are talking to these women. The mixer is meant for that. What should I be doing?