For a bus station, you might want something more like:

vehicle=no + bus=designated

rather than psv=yes, as it's more specific and excludes taxi/PHV using non-UK specific routers.

The existing motor_vehicle=designated tag (not added by you) is almost certainly wrong and should be deleted. I think the person who added it mistakenly thought that it meant "for designated vehicles only", but what it actually means is "designated as a right of way for all motor vehicles".

I can't find any street-level imagery, but if the sign at the entrance from Station approach is no entry with an "except buses" plate, the above should work. If it's something different I'll try to help you to find the best tagging here.

I have also added a section to the Busmiles.uk page on the OSM wiki.
https://wiki.openstreetmap.org/wiki/Busmiles.uk#Tagging_service_roads_in_bus_stations