Is it better to leave it bandaged all the time or expose it to the air a bit?

Any other tips for what to put on it, etc?

Neosporin, Air, and Brown Party Liquor

Aloe vera gel works miracles. Put a very liberal ammount on a gauze pad and tape it on with sports tape, not first aid tape. Try to tape it on in such a way that it doesn't squeeze out the gel.

Leave it on the majority of the day. Leave it off long enough for the wound to start to dry a bit, but be careful to keep it clean when uncovered.

Aloe is anti-bacterial, so you don't need OTC antibacterial creams.

Definitely aloe vera at first. Also try Climb On cream (sold at REI) and a bit of tape once it heals a bit.

this gonna sound really wierd...

nipple cream. get nipple cream for breastfeeding mothers with lanolin in it. it works great for rope burns and flappers. try it.