I don't know any specifics, and I might very well be assuming too far on the conservative side; but...
She was new to the football office, Petrino is a welcoming and friendly person, maybe they actually had a friendly, innocent conversation about his motorcycle and how she has never been on one...
Maybe, just maybe, this was two coworkers having innocent fun out of the office. Maybe he didn't want to volunteer her name because of rumors that might pop up. The fact that they work together is significant reason to believe it is an innocent relationship. She wasn't a stranger he found at the bar. (I feel like I'm talking to my wife

)
I've given students a ride to games in my car, absolutely does not mean I'm sleeping with them!
However, I don't know the whole story. And I definitely don't know enough to assume he's sleeping with her.