Years ago I bought a fanny pack expressly for this purpose. I used it for biking and jogging. At one time I carried an NAA Mini-revolver in the pocket of my jogging shorts and besides bouncing around and annoying me it was really going to be hard to reach and use (ever try to cock one of those when you're out of breath?

).
What I bought at the time was an Uncle Mike's fanny pack that has a holster-type arrangement inside and opens by pulling a thick, knotted cord - it works like a charm. They make other kinds now that probably work equally well. You can run with it, bike with it, etc. I had a patch sewn on the front to give it added color (it's just grey) and make it look more casual. It's an oval patch and literally says "GAYHEAD CLIFFS - MARTHA'S VINEYARD" and looks like this picture:
Martha's Vineyard Beaches - Aquinnah and Cliffs of Gay Head
Martha's Vineyard Tour Guide © 2017. All Rights Reserved.
Better than mil-spec camouflage!!! Totally innocent looking and inside it ALWAYS has this Colt Cobra (lightweight, snubbie, easy to hide, easy to shoot - any J frame would work, also).
Here's the theory. When you are riding a bicycle you are never as focused on threats as you might ordinarily be because the bike itself requires focus that walking does not require. Your hands are busy, too. If you are confronted, however, and assuming you can dismount, you don't want to have to go digging around for your gun. Pull that ripcord and VOILA!! GUN!! If you can't dismount it is even more important that you have easy access to your gun.
So whatever method you try, the key is ACCESS.