where can I buy a new trim for my bath plughole?
Before you replace it, you may just need to take the fitting off and reseal it.

Every fitting is different, most hold the screen on with a screw and then the fitting itself unscrews from a thread adapter on the drain pipe. Once its off scrape off any old sealant. Make a 'snake' (like you did with clay as a kid) out of plumbers putty and lay that as a ring around the drain fitting. Screw your drain fitting back in and wipe up the excess putty.

How old is old? 10 years? 15? 20? 50? 100?

Pics would help.