First, take a camera you are ready to crash with. Ha ha, but seriously. I sling the Rollei 35s on my wrist as it was intended, two hands for the bike, easy to ride/shoot one handed. (In another decade I would have relied on no hands riding, but after detaching my ribs in a crash caused by a road with lousy concrete joinery, I don't like to fall at age 60.)
I just sold my backup GRD, but that's another easy option. My Grd4 rides on a long metal necklace, also easy to grab shoot one handed. Bandolier style loop straps also good: I have a big Luma from pre- lawsuit days, adjustable length to sling tight (otherwise the camera bounces off me), tripod bushing attachment, strong enough for bigger cameras, but still easy to bring to the eye on the move if that's important.
For real fun duct-tape a Rollei set for infinity f11 to your forehead. Just leave clearance for the film advance. It'll look like you're really thinking every time your hand goes to your head. Or a salute to your subject, which is an attitude worth carrying into most photography.