This is a good question. Based on the following definitions, it appears that a bicycle is excluded from the requirements of a motor vehicle. However, the law requires that anyone approached by an officer (even outside of a traffic stop) must notify the the officer that they are licensed and carrying a firearm, if they actually are carrying.

These definitions are from Ohio Revised Code 4511.01:

(A) "Vehicle" means every device, including a motorized bicycle, in, upon, or by which any person or property may be transported or drawn upon a highway, except that "vehicle" does not include any motorized wheelchair, any device that is moved by power collected from overhead electric trolley wires or that is used exclusively upon stationary rails or tracks, or any device, other than a bicycle, that is moved by human power.

(B) "Motor vehicle" means every vehicle propelled or drawn by power other than muscular power or power collected from overhead electric trolley wires, except motorized bicycles, road rollers, traction engines, power shovels, power cranes, and other equipment used in construction work and not designed for or employed in general highway transportation, hole-digging machinery, well-drilling machinery, ditch-digging machinery, farm machinery, trailers used to transport agricultural produce or agricultural production materials between a local place of storage or supply and the farm when drawn or towed on a street or highway at a speed of twenty-five miles per hour or less, threshing machinery, hay-baling machinery, agricultural tractors and machinery used in the production of horticultural, floricultural, agricultural, and vegetable products, and trailers designed and used exclusively to transport a boat between a place of storage and a marina, or in and around a marina, when drawn or towed on a street or highway for a distance of no more than ten miles and at a speed of twenty-five miles per hour or less

(G) "Bicycle" means every device, other than a tricycle designed solely for use as a play vehicle by a child, propelled solely by human power upon which any person may ride having either two tandem wheels, or one wheel in the front and two wheels in the rear, any of which is more than fourteen inches in diameter.