Is there a brand name on any of this? That would help .
Is the water coming out of the tub filler, or out of the handle?
Sometimes all you need is to replace a washer, but sometimes the seat (the metal part the washer pushes up against to shut off the flow) needs to be replaced as well. Sometimes, it is just easier to replace the guts of the faucet. And, what may be the best solution, is to replace it with a new one! This can be messy, since it usually entails some new tile work.
The guts of many faucets can be replaced. You'd need to turn the main water off, then take the guts out of the faucet to a good plumbing supply house (you MIGHT be able to find the guts at a place like HD or Lowes). By having the old parts, you can match it up with new ones. This takes some skill, but once you have the new guts, it is pretty straightforward replacing it.
To take (most) faucets apart, you turn the nut that surrounds the handle (called a packing nut) counter clockwise until it is loose. Then, you turn the faucet handle as if you were going to turn the water on and it should back out of the guts of the faucet. Take that part to the store, and get a replacement. Put it back in in the reverse order (have the guts so that it is not fully seated while you screw down the packing nut). Note, the new part will not usually include the handle, so you need to either remove your old onces, or buy new ones at the same time as you will not be able to get the packing nut off to reuse unless you take the handle off.
One of the pros may have some other ideas...