I have nothing to say about her old relationship, useless information. But to start a convo and bring in the are you single question of the day I myself was a boy I'd say it like this..

"Hey, (Her name.)"

"Hey, (Your name.)"

"So-o yea it's (make up an excuse for convo, it's hot, it's cold, it's boring, it's a nice day)

"Yea. Blah, blah, blah"

"Yea, I know. Hey, what are you doing for lunch break? Want to have lunch together?"

"Yes/No"

"Yes" scenario:

"Oh cool, so are we staying here or going out?"

"Which ever one is best to you, but I mean we aren't dressed at our best" She giggles..

(share a laugh) LOL

End Of Yes Scenario

"No" Scenario:

I'm sorry I have to go, I'll get back to you in a minute!!!