I've used a cheapy Uncle Mikes for many years while bicycling or jogging. It doesn't look like a gun bag, but has a hidden compartment in the back that's accessed by just pulling hard on the front. I've had it for probably 15 years now and its ragged but functional. I even went down on my bike and skidded a small hole in it in '06. I've carried a j-frame/LCR in it for the most part, but a Sig P245 is what currently resides there. I've had to access it quickly one time when a pit bull decided I looked tasty and got me on the left arm. Even under surprise and with an angry dog to contend with it was quick to access and let me deal with the situation quickly.
I have no experience with any other fanny pack.