I had a class with her last quarter and we got along somewhat well. It was mostly just an acquaintance kind of thing where we were friends in that class but we don't really hang outside of that.

The situation now is that when I see her in the halls, I'll tap her on the shoulder and continue walking past her. She'll look at me then I'll turn around and say hi and she'll say hi and then I'll continue walking away. I really wish we were closer.

I was thinking since I don't see her regularly. I was thinking next time I see her I would say hi. Then like later that day I could text her saying "When was the last time you went out on a date? Simple coffee date this Sunday."

Thoughts?

Doing something is always better than doing nothing. But it might be good to firstly build some rapport before straight up asking her out.

Yeah it's always the question wether to go direct with girls from your class or not. When she rejects you, it's hard to have a good comeback.
That's why I always prefer to have a good connection with her, so when you 'ask her out', you'll have a better probability to have a positive outcome. (Ofcourse I don't know if you are literally only tapping her shoulder every time and only saying 'hi', because that won't be sufficient unless you're a stud)