plumbers must be asked directly what they charge hourly and if that is in addition to a service charge. The two are separate and I think they have gotten away with outrageous charges because of the potential of water damaging homeowner structures. I had a plumber (not Home advisor) come and replace a part in my kitchen sink that was under warranty---the spray nozzle had been leaking...He charged me $85.00 for 15 minutes of work and I will never use Mr King again.
Sometimes a faucet leak can be stopped by replacing the rubber washer at the end of a faucet stem or cartridge. This is a more common repair on older fixtures when things were built to last and designed to be able to be maintained. Other times the whole stem or cartridge needs replacement or the bibb seat deeper back into the fixture needs replacement. That leads to matching up the right components and often times making a trip to the hardware store or plumbing supply house necessary due to the many varieties, makes and models of faucets. My advice is to make sure your Plumber has faucet repair kit on their truck before having them come out to assess the issue.