What causes the front right springs or strut or bump stop to make light tapping noises as you go over bumpy roads?

It depends on the suspension type, it could be trailing arm bushing, strut bushing, shock bushing... Jack it up, get the tire off the ground, then use a long bar or 2X4 to move the tire up and down while you or a friend watch to see if there are any loose parts. Don't get under a vehicle that is up on jacks or even jack stands if you're playing around with the 2x4.