I'm more worried about running into a pot grow or meth lab operation than I am with aggessive 4 legged critters.
I've bowhunted hogs twice, taken 2, and one (a 100 lbs little squealer) came at me on the follow up. He was hurt pretty bad and I was able to get an arrow off (from a compound, no less) and then I set a record for the 100 yard Mesquite Dash. When I went in again I found that by pure luck, the second arrow had hit him between the neck & shoulder and did the job. Even if I had a handgun I don't think I could have gotten it out and put rounds on target in time, and I carry one for a living.
Conversely, I was later in on a follow up with the ranch owner on a non-fatally hit 200 lbs sow (no, I didn't shoot it). When the dogs caught up, it was a bloody fight that I don't have words to describe. The rancher dove in and cooled that beast with two contact shots from a 357. Had that pig targeted me, I wouldn't have stood a chance in hell of stopping it with the bow in my hands, and there was nowhere to run.
This hunt, BTW, was the beginning of my change from the Dark Side. The rancher was a Trad guy who shot a beautiful Palmer recurve. During the week of rubbing shoulders with him and hunting hogs with a compound, I began to see how much better a hunting tool Trad was than compounds.
As an aside, the ND legislature just this year passed a law whereby it's legal to carry a handgun while bowhunting. This was in response to the boom in the cougar population and the attendant incidents of bowhunters bumping into them out in the Badlands...
I share Matthew Quigley's opinion of handguns. That being said, I do have a S&W Mountain Gun in 44 Mag. It's about the perfect pack gun, and if I were to carry a bellygun while bowhunting, this would be my choice. It's light, compact, carries easily on the belt either crossdraw or behind the strongside hip, and has plenty of stopping & firepower if something goes south on me...