How cities came to decision to allow bicycles and/or motorcycles to enter bus lanes?
This is not a definitive answer, but it's too long for a comment. 

The primary purpose of bus lanes is to allow buses to move (more) quickly through peak hour traffic congestion. A bus carrying 50 people is using about the same road space as 3 cars when moving.

It's also a political statement to car users: take the bus to get there quicker. 

If we allow other vehicles to use the bus lane then 


The other vehicles must not slow the buses down. 
The other vehicles must also make more efficient use of road space than cars. 
And the message should be consistent. 


In a traffic mix where motorcycles are less than about 3% of the traffic they will probably not impede the buses, by my guestimates. Another solution is to allow the motorcycles to filter through stationary traffic.

In a location where the buses average 20 kph then cyclists are not likely to delay buses unless there are many more cyclists than buses. This case would be rare, but possibly occurs in a few places in Western Europe. In these locations there would be no benefit in mixing cyclists and buses. 

More common is the case where the buses average 40 kph and cyclists are rare enough that the buses can pass in reasonable safety. In this situation mixing cyclists and buses makes sense in policy terms, because the three principles mentioned above are supported. In practice the bus drivers need training to mix safely and consistently with bicycle traffic. 

So it's about the relative frequencies of the vehicles in the traffic mix, and their relative speeds.