First FR, just wanting some advice on what I should do moving forward.

To sum it up, I went on a first date with a girl to a party (mistake #1, I let her choose the venue), went okay but wasn't feeling a connection - too much socializing with other people. Went to grab a beer, came back and she was talking with another dude, intimately close and decided I didn't really want to bother with it. If she's not feeling it, that's fine. I start to do my thing, and after a k/# close I run into an old hook-up and I go home with her.

So I'm not doing a good job of describing this scenario, I know, but is there a way to get back with the original girl? I felt like I ejected from it too early, and didn't do a great job of showing interest in her - thus her talking to other dudes. I'm thinking of just texting her something like "hey, last night didn't really go as planned - how about we try again where it's just the two of us? [date/time/place] sound good?"

Any thoughts are welcome.