Not sure if she likes me

I've met this girl in one of my classes about a month ago.
I only see her once a week but we've spoken every time, got her number, messages on facebook and went for drinks with a whole group twice.
When we were finally alone the last time I tried to ask her out but it didn't go so well. This is kinda how it went

me: any plans for tonight?
her: no, no plans
me: so would you like to do something sometime?
her: tonight?
me: no, maybe next week?
her: I don't know
(this was in the afternoon after a couple of beers btw)

After a small moment of silence other people from our group came back so I dropped the subject and didn't mention it again. Unfortunately I didn't get to talk to her as much as I wanted to because it was a big group. At the end she gave me a hug and said we'll talk on facebook.
Before I asked her, on facebook, she invited me to an event but also a bunch of other people (1gay guy and the rest all girls)
I made a comment on her status about the event she was going to and then she sent the invite to me and the others, didn't send me a message about it though.
So I'm really not sure what she thinks. She does have some plans for next week but could also mean "no" but just didn't want to tell me straight up.

I'ts hard to read her body language cause she's an extravert person and might treat any guy the same. She gives me mixed signals, ignored me a little bit the last time and was more busy talking with the girls in the group.

I was thinking about just sending her a message on facebook and asking to go for drinks on a set date to get a clear answer. Would like to do it in person but a break is coming on and I won't get to see her for awhile, only one more time and might not get the chance to talk to her alone.
Should I just take a risk and send a message?
I'm not sure if she is just being nice cause I've been wrong before with another girl who, which I later found out, already had a boyfriend and just wanted to be friends. (She is single)