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!!!