After giving this a lot of thought, I think the real problem is the rider's legal status when he gets off the bike for a break. He's not allowed to carry the handgun with him, so it would have to be transferred to a secure location on the bike and left there until he returns. The only exception would be if he's going to a residence, such as a motel or (maybe) campsite where handguns aren't prohibited. Of course, with a permit, none of this is a problem. I just hate spending the time and money to satisfy what should be my constitutional right in the first place.
As for long barrel firearms, I don't have a use for those on a bike. It's not my intent to scare people off en masse. In all the years and miles I've biked, there's never been even a close call. It's just that things in general seem to be more violent now than 30 years ago. I'm thinking more about the types of situations that can occur if you break down on the side of the road late, or as someone else mentioned, if you go camping. I've always been self-reliant when travelling, and even today, I don't carry a cellphone.
Thanks for everyone's ideas on this.