I ride about 150 miles per week, commuting to and from work (50-mile round trip, though I can take the bus for part).
In cold weather, I carry my Ruger LCP in a pocket on my jacket. That works very well and it's quite accessible. The pocket I use is at about 4:30 and angled just right -- zip, grip, draw.
In warmer weather... I haven't found a good solution. I tried a SmartCarry, but it chafed. Bad. I like my SmartCarry, but it doesn't work for me on a bike. I experimented with a fanny pack, but just didn't like it. So, I carry in my backpack, or if I'm on the bike with a rack, in my panniers. Both of those are comfortable and easy, but they're ways to transport the gun, not carry it, because it's not accessible.
Four boxes protect our liberty: soap, ballot, jury and ammo. Use in that order.
Utah CFP Instructor; NRA Certified Instructor for Pistol, Rifle and Self-Defense in the Home; NRA RSO.
I am not a lawyer!