If the buzz comes from nearby, that's a pump in the shower -- a so-called "power shower". Like computer fans, small pumps are noisier than big ones. (My shower screams like a turbine.)

It's possibly also to do with the fact a power shower pumps "new" water the whole time -- unlike a heating pump which pumps the same water round and round a closed system -- which means that it's more susceptible to limescale and other corrosion or deposition, causing noisy operation.

Some power showers are also heaters, but most just pressurise hot water from a tank system. (You can't have a non-heater power shower with a combi boiler, because you'd be pumping mains pressure, but conversely you don't need a power shower with a combi boiler, because the hot water is already at mains pressure.)

Peter