Out of interest, are the electrics they are quoting going into the vehicle harness and activating an in-dash indicator and buzzer (vehicles tend to have that kind of thing now)? Or are they proposing using the old-fashioned 'traditional' way of tapping into the lighting harness?
Also, you say "13-pin" as opposed to the 7-Pin style. Will they be fitting a fully-wired 13-Pin socket, complete with all the wires needed for a caravan, or just wiring suitable for a basic trailer/bike carrier? if you don't need/want the full wiring monty but want the better reliability of a 13-pin socket (which makes sense), then there could be room for price discussion there?
Overall, the price you've been quoted sounds pretty reasonable to me. I've tended to fit my own towbars, but thinking of the time needed to fit and the parts, it is around what I would expect to pay.