If retrieving your camera from a bag is too much work while you're strolling around shooting, Sun-Sniper's Strap-Surfer might be just the ticket.
It's a short strap with a tripod mount that connects to your camera on one end and your bag strap on the other, via an ingenious two-part magnet that interleaves to provide a smoothly sliding attachment. The strap itself is sturdy webbing reinforced with stitched-in steel wire down the center.
This isn't a strap for everyone: it's a nice idea, but can be awkward to use as a full-time strap. I leave it attached to my Shootsac (a lens-only bag) for days when I'm just going out to shoot and won't need to stow the camera at all.
In order to most effectively use the Strap-Surfer, you need a bag strap without any padding on it; for instance, the neck pad typical on a messenger bag's strap will interfere with the Strap-Surfer's ability to slide up unimpeded if you've got the bag against your lower back. Backpack straps are generally too thick.