The key test is whether the bus lane sign has the word 'local' in the bus on the sign. If it does, then the lane is restricted to buses on a scheduled service. If it doesn't, then a 'bus' is defined as a vehicle having more than 9 (from memory) passenger seats. This is why Lothian Buses use a Transit minibus as their 'Green Lane Patrol Vehicle'.
Some of the lanes around the Shandwick Place tramstop and the West End have 'local' on the sign. Most of the lanes in Edinburgh don't.
I have an unhealthy interest in this due to my involvement with another group that runs a minibus. We like to know where we can (and can't) drive it.