All the double-decker buses in our area have the height just above the top of the windscreen.
We regularly travel across the Channel with bikes on our roof, so I have the total height in Inperial and Metric fixed to the back of the sun-visors.
just had a look at that one, webbo, and there's a standard triangular sign saying 13ft 6in overhead on each side of the bridge itself, and another about 100 yards back on lamp posts. They're there if you look for them but I can see a driver unfamiliar with the town might miss them (the bus doesn't seem to have any insignia so it may be private).
What you really need is big warning signs saying NO DOUBLE DECKERS or something like that.
Why would the bus-driver take a different route? School- bus drivers are assigned a definite route since they pick up kids at designated points in the morning and drive them to school, and in the afternoon they reverse the route and drop the kids off at the same points.