Filming a Bike From The Angle of The Wheel
Buy an action camera (GoPro, SJcam, Sony, knock off brand) and use one of the many accessories you can get and or some fancy duct tape work. This way you would be able to get closer to the frame and also use the camera for some other more artistic shots due to the size. 

Otherwise you could build a rig using clamps and rods to support your main camera but this could make the bike side heavy and not as easy to ride.

I think the professionals (hollywood films) would probably build a side frame for the bike so the bike is more stable