the overall interaction went well, it could have gone better in my opinion though. she deffintly seems into you. this is probably what i would have done(i root alot of my responses with sex, so this might not be the style yoru going for) thee diffrent routes i might have taken it:
A-when she said sorry and that she was very busy, i would have busted her balls on that. probably siad something like "excuses, excusesss. theres no such thing as being too busy for ALLL this. just admit it, your overwhelmed[/intimidated] by how attracted you are to me

"
b-when she asked how she could make it up, i would have brought a bit of sexual tension into the situation: "well theres this one way...but, your too much of a good girl to be any good in bed, so ill just let you get me some coffee tomorrow at XXXX"
c-when she said she doesnt think so because she has too much homework: "uncertainty is very unattractive, ill let you slide this time, but next time your gonna get a spanking" or "i almost wanna feel bad for you, but than i realized your teacher probably hasnt gotten laid in like a trillion years, so shes trying to fuck all of you, only with homework. you should let her know for future refence though, i got that area covered

"
again these are off the top of my head rough ideas that shoudl be phrased slightly diffrently to tailor the situation. also i take a diffrent approach than it seems like you do. hope they help.
about re-initiating- theres no need to try use a fancy opener or method for reopening, she seems into you, a simple hey will cut it, if you wanna use something diffrent you can open with something like, "i just met[/saw] your twin" or like "i know you cant stop thinking about me, so i thought id say hi"...or my personal FAV "made you look"