you can't win - if you'de just called it the Forth Bridge* - it would have been brought up with the search to prove that since 1964 with the Fourth Road Bridge along side it - that it is the Forth Rail Bridge.
(*pedantic - marked by a narrow, often tiresome focus on or display of learning and especially its trivial aspects)
Do you ever admit you are wrong? I do admire your tenacity even if irritated by it! It was the Forth Bridge but now, to distinguish it from it's neighbour, it is the Forth Railway Bridge and the analogy with films is irrelevant.... But you won't agree!!
When the railway bridge over the Firth of Forth was built it was called the Forth Bridge.
When the road bridge was built it was called the Forth Road Bridge and the original bridge became colloquially known as the Forth Railway Bridge. which has to all intents become its accepted name to the extent that the bridges own website calls it such.