Just watched the Captain America film. It was freaking awesome. I can't explain how good it is. I urge everyone to stay after the credits!
SPOILER WARNING: Click here to reveal hidden content.Although he shows great H2H skills it is never shown who trained him or how he knows how to fight...
Bruce was shown to be trained in H2H. It's experience vs super soldier.
Round 1: On their motorcycles in an empty New York. Cap has his Shield mounted to Motorcycle.
Round 2: H2H in boxing shorts
Round 3: With standard gear in movies.
EDIT: Adding round 4
Round 4: Dark warehouse with dim lighting. There is a light switch that will kill all the lights but it is about 200 feet away from their location. They start 50 feet away. Batman knows Steve is a SSS. Steve doesn't know Batman's technology but doesn't know the way Batman fights.
Round 5: Do rounds 1-4 with any current versions