What type of tub is it? Free standing or one with a panel on the side?
If one with a panel on the side you can remove them by cutting the silicone, which will enable you to see the drain pipe and the trap, and you can then inspect it for leaks (use a dry piece of paper towel to test if a leak continues after drying it initially)
If it’s due to a leak from the water supply pipes you could try turning off your water at the source/stop tap, open up your all the taps in the house and drain your system (I wouldn’t suggest doing this if you have a water storage tank). If the dripping stops after doing this, it’s likely to be your water supply pipes, as opposed to the drain.
Straight out of Alexander Dugins book…