One thing Ive noticed with a lot of guys is they freak out when a girl is busy. It is the 21st century - EVERYONE is busy. You must be busy also. If not with work then dating other girls or having fun times with your mates and experiencing life. Try not to fall into the habit of questioning her schedule, commenting on how busy she is or discussing her projects because it makes it look like you are hanging around bored all day. You want her to reveal her feminine side, not her masculine workaholic side and vice versa. It should be HER that role plays her motherly/caring/empathetic fantasies on you.
If you try hit her up for another date you could qualify your own schedule first and how busy it also is 'Man this week is nuts, 12 assignments, 24 exams, 245 classes in 2 days, yoga practice, need to fix my motorbike, need to buy new guitar strings for 7 different guitars...girls asking me out for dinner...I'll be needing a mojito by the end of the week!' (I'm being funny, not saying you should actually write that) or ask her out in a group dynamic like she did 'Hey were going to this place, its going to be off the hook, you're coming'. That way, even if she can't make it, she will know you're out ANYWAY and possibly around other girls. You can also simply ask her when she is free. Be bold and uncompromising in asking for it. Girls who are interested will always make a tentitive date at the least. If she is totally like 'I dont know, I'm not sure, I have so much on blah blah blah', she is probably not someone you want as a girlfriend anyway right? She is not an astronaut.
Most of the time it is men that have to initiate. Most of the girls I know who initiate a lot are either very talkative and chatty by nature or are desperate to get my attention because they know I have lost interest. I like initiating. Sometimes it doesn't have to go anywhere, its just friendly messages to make each others day better, keep re-inforcing attraction. As soon as there is any opportunity towards flirtation or meeting up I pounce on it. I am also quite often busy and will even forget about girls on my phone lists. Some girls things happen within hours, other times within weeks. It doesn't matter as long as the end result is the same. Don't worry so much about what she is doing and just concentrate on yourself having a blast. Always have other women in the pipeline to date to keep you in balance. Women seem to have a 6th sense for that and amazing things can happen from jealously or knowing a guy has lots of girls after him.
I never really talk with a girl about being 'exclusive' and certainly wouldn't even think about any of that until you have slept with her. Girls are usually the ones that raise that stuff anyway so don't think about it until neccessary. You can bet she probably has other guys in her life too but don't worry about it. Stay confident about your ability and keep demonstrating it.
Keep building attraction and as T-Mal said start again with a fresh approach. Lock her down for a date this weekend or next week and make sure you Kino escalate towards full kiss/fark close. Ask her out in a way that has time constraints 'Catch up for a quick coffee, I have something else on later but I can see you for a little while'. Kiss close. If she keeps putting her schedule in the way and won't give up any time at all, completely freeze her out, never re-initiate until she does and move onto other girls who are better at managing their schedule.