Earthing the bath isn’t necessarily a good thing, it makes it more likely that an electrical fault will use you as a bridge to ground. All metal services coming into bathrooms are now linked together (in new installations) with earth wire (called equipotential bonding or something) to prevent this happening. So all the water pipes are directly earthed to the light fittings/switches.
The regs (last time I looked, I’m not a sparkie) actually state that a kitchen sink should now not be earthed at all, due to the risk you will be touching the sink and a faulty kettle at the same time. You don’t want to be the easiest path to ground! So I ignored the sink instructions to connect it to earth 🙂