Ah, it's a tough situation. It's not like you run into her anymore and people that matter usually don't get the I'm busy and all that. Every time. It'd be different if you ran into her again and had a fun little chat and you could gauge her reaction from that. Over AIM, it's tough. With somebody you aren't close to, it's difficult to be spontaneous as well (since she is so busy and all)
It's your only option though. You could either do it or not, hoping somewhere down the line you run into her by chance. How can you handle that
The keyword is acquaintances. How do you catch up with somebody you didn't know that well in the first place?
I would ask her to do something sometime on AIM, and just say that she seemed like a nice and fun girl and you'd love to hang out sometime and get to know her better.
Are you having a tough time with the dating world right now? To go for an acquaintance seems like a stretch. I've been broken up for six months and I'm a bit desperate myself and it's really ruined my chances with girls that even agreed to go on dates with me. Then again I suck at being myself but still, just curious.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.