Hey bro!
Yeah i definitely think it'll be bad idea to bring her break-up up, im like dude she hardly knows you and it'll be major creepy. So heres what i suggest go make a funny comment on some pics of her or on her status.
Be cocky, funny and different.most guys will comment on a girl's looks or something like that so id advise you to go more indirect. example : "lol thats one badass hairstyle, are you also badass? or is it just the hair?

"
Only then open her in facebook chat. lol a funny line i've recently adapted that works wonders and it's Facebook field tested is " I heard on the news someone checked into the pysch ward wearing only a thong and riding a goat. I'll come & get u.... BUT THIS SHIT HAS 2 STOP!!!!" that always get them cracking up, and then I just transition from there.
Heres a technique a guy called Brian Bond uses and I tell you what it's golden for facebook pick up and setting up a 'Hang out".
Quote:
ME- Red or black?!
SHE- what?
ME- Red or black... its an easy question... just answer!
SHE- depends on what you are talking about
ME- oh gosh, let me make an easier question then: Hot or cold? ... JUST PICK ONE
SHE- Hot
ME- odd or even?
SHE- odd
ME- i thought soo... Radio or TV?!
SHE- TV
ME- WRONG... nice meeting you Miss Hot/Odd/TV, but there is a conflict on our personality! >:-/
SHE- lol ... ohhh nooo ... let me try again!
ME- Last chance... Coffee or milkshake?
SHE- Milkshake
ME- uhmmm... i can deal with that...
SHE- Yeahhhh
ME- Today or tomorrow?
SHE- lol ... today
ME- You pick the place or i pick the place?
SHE- lol ... you pick the place
ME- 8PM by the soccer field
SHE- Make it 8.30 ... see you there ... you are too funny!
Take note that i dont do this unless i got some sort of REPLIES (PLURAL) from her on a picture comment or status or something. Also, make sure she knows who you are, that at least she as seen you on campus and you had at least smiled at her and got a positive response. Dont be suicidal and open like this to a completely random girl!
Hope this helps bro.