I really appreciate the advice.
I cut open the kitchen ceiling to remove the water, and get a better idea of the problem. Turns out it was the bathtub.
Then I had to cut open a section of wall in the bathroom because there is no access panel; the copper pipe connecting the hot and cold apparently has a small split, causing the leak.
Finding the problem is 3/4 of the battle! Now, to replace tub faucet, install access panel, and fun-filled drywall & painting!