the short answer is yes, you can put radial tires on a motorcycle, and there is nothing unique about a motorcycle design that requires it to have bias or radial tires.
The long answer is that radial tires are the standard for racing bikes. You may or may not like having radial tires on a touring / cruiser bike.
If you google the subject there are many web sites that explain the differences between the two on a motorcycle. You could spend hours reading about it.