Mitch,

I would assume you are refering to your up comming bear hunt in Maine. Maine regulations allow ou to carry a side arm while bow hunting deer although you can not dispatch the deer with it. The only mention of special regulations for hunting bear and possessing a firearm are as follows.
Note: A permit to carry a handgun to track wounded bear after dark may be obtained from the Warden Service Headquarters
There is no "bow season" in Maine for bear. There is a general hunting season, Baited season, and hound season.

http://www.state.me.us/ifw/hunttrap/...%20INFORMATION

I've never read of a bear attack occuring in Maine after a bear had been shot with an arrow. For that matter I can't remember the last time I read or heard of a bear attack in Maine. I'd personally be more worried about the moose population as they have been known to charge people / hunters on occasion.
Bottom line, if you feel more comfortable with a sidearm bring it along.

Happy hunting