The bridge has been proposed in the past, but was rejected as it was deemed unnecessary for the amount of traffic in the area. The RoR was too low for it to be an attractive proposal.
Normally, constructing bridges is an expensive venture. But constructing such a long bridge, that too over a sea, will be prohibitively expensive. The benefits too aren't much. Most of the passenger traffic in the area is towards Ahmedabad. And major places like Rajkot, Gandhidham, Jamnagar etc won't really have any benefit because of this route. With...
more... the money required to construct the bridge, the capacity of the entire line between BRC and Viramgam can be increased and with money left for other operations.
However, the Indian government is planning to construct a dam across the Gulf of Cambay (estimated to cost Rs. 90,000 Crore, but will definitely end up costing at least twice or thrice that), starting sometime in the 2020s. If this dam is ever constructed, then they can run a railway line on top of it.