you could try to use a handheld dslr steady mount
the camera sits on the mount and gimbel and has a piece that curves outwards and down with a counter-weight at the bottom
remove the handle grip and replace it with a bolted on piece of wood, or clamp it to a c-stand arm and onto your bike
**the pic is of a super cheap consumer version, not sure if this particular model is smooth enough. in the end it all really comes down to how much you wanna pay.
Smooth = Expensive**(edited)