Yeah, she sounds super busy.

In general, you can always say something like, "hey, me and my friends are gonna go to the bar. wanna come with?" It lets her meet all your friends if she doesn't know them already. It shows that you wanna let her into your life a little more. Makes her feel more comfortable.

I would say give it a week, though. See if she texts back. If she doesn't text back, I would say something like, "hey i just wanna say I had a lot of fun on our date last week." (Obv you told her this already, but it's just a way to ease into the convo.) Then she'll probably say something like, "yeah, I had a lot of fun too!" Then you can say something like, "cool. let me know if you wanna hang out again sometime soon." That puts the ball in her court without seeming too pushy