Still puzzling over the bridge enigma, I decided to try asking the Bath Tourist Information Centre. I received a very prompt and helpful response from Kirsti who works there. She told me that the Pulteney Bridge and the Ponte Vecchio Bridges are the only two bridges that are originally designed to have shops on them: the Rialto Bridge was not originally designed to have shops on it.
She goes on to say, "However I have located the following site which does refer to the four Bridges you mentioned on your email, please see attached link:
Here it mentions that the fourth bridge is located in Erfurt Germany ; http://www.kraemerbruecke.de/index_eng.html
Please refer to the following site for an picture; http://en.wikipedia.org/wiki/Kr%C3%A4merbr%C3%BCcke
I hope this is useful for you."
Well, indeed it is, it has certainly helped assuage my curiosity.