Don't spend so much time focusing on "asking her out on a date", but rather getting to know her and doing stuff together ideally in a one-on-one setting. Don't put yourself in the position to get a "no" just because she doesn't know you - give her a chance to get to know you... if she likes you, you'll know.
What to talk about applies mostly when you're on a date... or when talking with her in a one-on-one situation. When in doubt, talk about her. Ask her about her day, about whatever... Jennifer says I can hold a conversation with a brick wall, and I guess that's a personality trait, but people love to talk about themselves. They love to see that you're curious enough to ask.
A big mistake guys make is always showing off by talking about themselves too much - that shows a lack of inner confidence. Instead, find out about her, her life, her job, her interests, her passion, etc... she is a real human being with thoughts and feelings on innumerable topics... there's always something to talk about.
If she's not interested in you, she'll let you know by seeming uninterested, rushed, and by leaving. Women are pretty good at discouraging men they're not interested in by simply walking away. If she's not interested, you'll know it.
Watch these videos for ideas to approach women:
How to Get Over Shyness & Fear of Rejection to Get the Girl
How To Escape The Friend Zone and Get The Girl
Leaving the Friend Zone - How to Actually Ask Her Out
Follow up here and let us know how it goes!
Dan