Bath, like the rest of Britain, uses standard British plugs with three rectangular prongs, known to a few as BS 1363.
BS 1363 plug http://upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Bs1363-non-earthed-plug.jpg/170px-Bs1363-non-earthed-plug.jpg BS 1363 socket http://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Basic_earth_pin_operated_shutter_socket.jpg/170px-Basic_earth_pin_operated_shutter_socket.jpg
If you've heard somewhere about Britain having different plugs in Bath, you (or whoever told you that) may have misheard: Britain uses different plugs in bathrooms. British electrical safety regulations are very tight, and normal outlets are not allowed anywhere near water. In a bathroom, you can only put BS 4573 shaver sockets. These sockets accept European, Australian, and sometimes (if a transformer for 115V is included) US plugs.
BS 4573 plug http://upload.wikimedia.org/wikipedia/commons/thumb/a/a0/ShaverPlugUK.jpg/170px-ShaverPlugUK.jpg UK shaver socket http://upload.wikimedia.org/wikipedia/commons/thumb/2/21/ShaverSocketUK.jpg/170px-ShaverSocketUK.jpg
Electric razors and toothbrushes (but not hairdryers) sold in the UK have European two-pronged plugs. They fit in British shaver outlets and in European outlets, but not in the other outlets in a British house.