Hi, so I just had this problem and went through the TOH forums and couldn't find an answer. I figured it out, but my answer won't work for everyone because not everyone has my type of bath faucet.
My bathtub fixture is 3 pieces, a hot valve, a cold valve, and a "diverter" or water faucet between the two. The diverter has a stem on top of it that, when you pull up on it, diverts the water from the bath to the shower head. Any time I pulled up on the stem, about half the water would come out of the bathtub spout and half would go to the shower head. Here's what I did:
1. Removed the "diverter". For my kind the whole thing unscrewed, others may find a small set screw or allen head usually on the underside of the faucet near the wall that needs to be removed. Also, there was silicone caulking around the seam between the tile and the fixture that I had to remove.
2. After I had the diverter off, I looked at the back and noticed there was a white, plastic insert that actually had the threading that attached to pipe that came out of the wall. I proceeded to yank this insert out of the metal casing using a channel lock. It did some damage to the insert because I had to pull pretty hard to get it out, and I was using a metal channel lock.
3. When I got the plastic insert out, I inspected the stem that pulls up to divert the water, and found that it was pulling a small valve that had a rubber washer which was broken. So rather than having a tight seal, the water was rushing through the break in the rubber washer. Off to the hardware store...
4. When I got to the hardware store, I couldn't find a replacement washer, but found I could buy a whole new diverter for about $20, and that at a local True Value so you know it's going to be cheaper at Home Depot. Then I took it home and screwed the new on, and re-caulked around the base using silicone caulk.
I'm sure if I had hunted hard enough I could have found a replacement rubber washer, but for me just buying a new fixture made more sense. I've attached a photo of what my fixture looks like, if you'd like more detailed photos of the parts inside just let me know! Hope this helps.