I have recently had a new bathroom installed, but the plumber did not
install supplementary bonding. I have decided to do it myself, but am
unsure as to where to place the certain earthing connections.

If the plumbing is all plastic, then supplementary bonding may actually
reduce electrical safety. However, if it is all metal, but with 30cm of
plastic tube, then it isn't clear whether or not you should bond after the
break according to the regulations. It is certainly recommended not to bond
if there is more than 1m of plastic. (BTW, the exposed metal pipework would
always be bonded, it is only the taps and bath/radiators that are in doubt
if insulated from the main pipework).

Note that electrical appliances should always be bonded. However, in a fully
plastic plumbed room, you may only have one such device and nothing to
connect it to.

Christian.