MOPED ARMY

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)