I ride just to get the heart rate up, give the lungs an exercise, and not let my legs atrophy.
My knees and ankles can't take running anymore, so hitting the bicycle is it.
Back in the '90s I'd put my Beretta Bobcat .22 LR in a fanny pack while riding the mountain bike I had back then. Nowadays, my preference is my Taurus TCP in .32 ACP in its pocket holster, but I wear somewhat baggy pants or shorts that make that possible. I'm not trying to be aero when I ride, that's for sure.
I figure anything that is Ruger LCP sized works just fine for cycling. Which actually is one reason a new version of a VeloDog isn't needed in the 21st century, IMO.
Although I could use a carry gun on a dog, I really carry because of people. Most dogs around me are not a stray pack, they are someone's pet. That was probably a lot different back in 1900.