19 y/o here
So you approached this girl in the library and she gave excuses when you went for her number.
Girls have only given me the 'I have a boyfriend' excuse when I go for their number. The excuse she gave you imo is serious bullshxt; you don't harass anyone, how cheeky of her. Hate that she slyly ignored your invite in the email aswell argh
I can relate to when you asked her out for a drink, coffee etc.
I approached a russian 22y/o girl in the street a month ago, got her number (she even suggested 'MAYBE WE CAN MEET UP SOMETIME') BUT...
she gave 3 excuses in a row before I dropped her:
1. I can't I'm going to scotland for 2 weeks and will be back

etc
2. sorry I have an exam so not until 6th april etc
3. I have lessons during that time etc
I was persistent for a month but she was actually just wasting my time. I'm not wasting my time on someone that won't give me any of theirs.
I deleted her number. I don't waste time.
This girl that is now looking at you frequently gets a thrill out of having power over you. That is all.
She loves the attention, not you.
She knows she's pretty so she checks who's looking to make sure.
She wants to keep you on the side whenever she wants some attention that's easy for her to get.
Ideally you should ignore her until she does something other than look good, and then ignore her some more but you don't get that much P**** lol
if you do decide to talk to her when you next see her, get to the point. Ask her out for a drink very quick
e.g. (im going for a drink on saturday if you'd care to join me)... dont overanalyse it she's already thinking about hanging out with you. Just bring it up again.
If she gives an excuse, don't say anything just look her in the eye calmly until she looks away.
what you're communicating is: whatever I don't really care anyway
I think when they give excuses all theyre really saying is
'whatever happens I'm not responsible'
..or it might be that they're not comfortable being alone with you yet... whatever
p.s.
asking how are you what you up to via text/email destroys attraction. don't do it. be objective.
talk to her about those things only in person.