I used to use a pencil cam that could either be powered by 8 aa batteries or could be wired to the bikes battery. This went to a standard mini DV camera in a bum bag, it was from dog sport cameras. Not sure if they are still made now that go pro and the like are so popular
The Drift HD Ghost S is a good little camera and can be bike powered but the remote is wifi, not wired. It's worth considering but might not meet your needs.