You're giving Batman a day of prep? That makes it easy. Batman. The answer to any "who can win between Batman (given a days notice) and [insert chump here]?" is instantly a Bat win.
In fact, give Batman a day....:
Check e-mail - "Oh some spider geek is wanting some throw down"
Notice all photos taken by Parker, but never two are in photo together
Work out Spider-Man is Peter Parker
Do some Bruce Wayne Stuff
More Bruce Wayne Stuff
Invent Spider repellent bat spray
Requisition universal solvent from Wayne Tech to deal with those pesky webslingers
Stroll Wayne Manor Gardens with Mary Jane
Bump uglies with Mary Jane
Tweet this to world on Bruce Wayne twitter account
Make excuses, leave and pretend he does respect her and he will definitely give her a call later
Do night based Batman stuff
Set alarm on phone - "9:30am - Remember to shove spray down teenagers throat"