I've noticed routers weren't taking people to the entrance, they went round the back to the paved area where the buses wait. 

I've made that access=no (except for buses) based on the signage and I've also added access tags to the "corridor" inside the building and included the bus station building in the bus station (before it was just the paved area outside).

The effect is that when someone puts Edinburgh Bus Station as the destination, routers will now take pedestrians through the entrances instead of round the back.

https://www.openstreetmap.org/directions?engine=fossgis_valhalla_foot&route=55.9519%2C-3.1904%3B55.9553%2C-3.1915#map=16/55.9526/-3.1907