The tub has one of these types of faucets. It's called a ball faucet and looks like this:
Instead of continuing to push down as hard as humanly possible on the handle, trying in vain to stop the dripping, I decided it would be a better use of my time to just fix the darn thing. After a little bit of research, I was ready to tackle this small project.
According to most of the home improvement websites that I visited, dripping faucets are typically caused by worn out washers and other rubber parts. This seemed to be a pretty universal reason for any type of faucet assembly (judging by my 30 minutes of internet research).
Here's a drawing of a ball faucet layout from Meriam Webster (good idea for them to branch out from being just paper dictionaries! You don't see too many of those anymore.) The handle's different, but the guts appear to be the same.
With this knowledge and schematic, I took the faucet handle apart and checked out the rubber parts.
From this previous project, I had all the replacement rubber parts. Since I was taking it apart anyway, I figured that I would just go ahead and replace the rubber pieces.
First, turn the water off to the faucet! If there's no handle, there's nothing to stop the water from flowing through the faucet assembly. I had to go under the house and turn off the main water line.
Next, I pried off the "H" and "C" cover with a screwdriver. This showed a screw, which I removed. The handle could then be removed.
I then used a wrench to take off the bonnet.
NOTE: Don't use too much force here. You don't want to damage the plumbing behind the faucet. If it's stuck, don't pull with all your might. Try loosening it up with a hammer.
This exposed the retainer ring, which holds in the first washer and the ball. Both can then be pulled out by hand. You can then easily access the washer and replace.
If you look in the remaining hole, you'll see the valve seats. I used a pair of needle-nose pliers to get those suckers out, along with their corresponding springs. I put the new valve seats on the springs and placed on the pliers for reinsertion like so:
I then stuck both back into the hole.
After that, everything was put back in its place. On reassembly, be sure the notch on the packing retainer ring goes into the slot correctly on the wall. Also, don't put the retainer ring too tightly. It should be fine with just a hand tightening. If it's too tight, the valve seats will get worn out faster and the faucet will be difficult to use.
The main water line was then turned back on and the faucet was tested.
No more leak!
Updated 2/23/2014 with a couple of small notes.
