Would you use Facebook to contact a girl you do not yet have a phone number for?

Here is my scenario:

Details of past

I've just graduated collage (I'm 22) and I'm living back at home and I work for my dad. I don't have a strong social network in my home town so I decided to hit up an old buddy from high school and he invites me to a party over the summer. I meet this girl with whom I hit it off with. Since i was simply being a pussy about it, I did not ask for a number. I didn't ask because she was going back to school in 3 days so figured "eh, shes not gonna be around anyways". But anyway, my buddy is good friends with the girl and I told him I'm interested so hes wingmaning for me as far letting me know when she will be around for winter break and such. As far I understand, from when I met her, she digs me. She was very friendly and interested in what I had to say and used kino on me several times. She also got very excited when she learned I can play (guitar) and sing one of her favorite songs.

I saw her again when she returned home for winter break at a Christmas party the Saturday before Christmas. I knew she was gonna be there so I was couldn't wait to talk to her again. She got to the party I greeted her, gave hug, asked how she was and such, she asked the same.

She went off to greet her friends and 10 minutes later my buddy is talking me up to her: saying I'm a good climber etc... I wanted to talk to her more myself and maybe get k-close that night, but she disappeared after only being at the party for like 15 minutes. I was happy that she actually remembered me from meeting me only once 5 months ago.

So my question you all is this: Should I send her message over Facebook to ask her to meet up?

Message Begin

Hey, I know this a bit random, but Facebook is what I have to work with because I've grown tired of waiting for the next opportunity to meet up again at party or what ever. I had fun talking to you at the party over the summer and I'd like to get know you so I want to take you climbing this week.

So if a random message isn't too scary, I'd like your phone number so I don't have to use Facebook :)

End Message

Any constructive criticism would be appreciated.