The pneumatic tire was invented for the bicycle. Bicycles have always used bias ply tires. Radial tires have been tried but they have a strange handling feel because they aren't as stable as bias ply tires laterally. So it is in practice impossible to find a bicycle using radial tires. Probably a factor in favoring bias ply tires over radial tires is the fact that bicycle tires must be as wide as they are tall for optimal cornering, so the advantage of radial tires for allowing tires wider than taller is not a consideration. Also bicycle tires with their large diameter and narrow width don't "scrub" the pavement as much as wide bias ply car tires, so the increased rolling resistance due to tire "scrub" is not a major problem.
Cars, on the other hand, switched relatively fast to radial tires after radial tires were invented as a replacement for bias ply tires. Today it is very rare to find a car that uses bias ply tires, and if a particular car happens to use bias ply tires, it is almost always an antique car.
But what kind of tires do motorcycles use? Bias ply or radial?