I went to Camping World on my lunch break today with the intention of buying a new tub faucet. They had some bins in front with clearance items and there was a sink faucet with shower hose attachment for only $5. Too bad that would look very strange in my bathtub. I went to the plumbing aisle and found the faucet that I needed for $38. Then I saw the handle replacements for $5.80. I bought the handles.
I figured I could make due with the handles for now and live with the drip for another year until I sell my RV. Maybe I'll find another faucet for cheaper than $38. Maybe I'll find one in the clearance bin. Maybe I'll just sell my RV with a leaky faucet.
So for now I will catch the drip in a small bucket and use the water for the toilet. Most of the time the water pump is off so it won't be dripping all day and all night, just when I am doing dishes or something like that. I am glad that little chore wasn't too hard on my budget.