Using a bolt, a few washers and a reflector mount salvaged from any bicycle shop’s trash bin, you can fashion your own handlebar camera mount for your bicycle.  If you can’t figure it out from this photo (you need a 1/4″ x 20 thread count bolt), you can get complete instructions on Instructables.com.
The bolt threads into the tripod mount screw hole on the bottom of virtually every camera made, then you tighten it on with the wing nut.