Master bath faucet leaks when using other showers or when running dishwasher
Assuming you have an anti-scald mixing valve then it sounds like the seal (gasket) inside the bathtub faucet's cartridge could be compromised.
When the water pressure is full force (no other faucet diverting pressure) then the gasket is being sealed by the water pressure but as soon as a tap is opened then it alleviates enough pressure for the tub valve to fail.
You probably need to replace the cartridge in the tub faucet.
Even if it's not an anti-scald valve you need to investigate the gaskets inside the faucet.