It looks like the bus driver made a recognised error called a foot placement error. After you've stopped you put the handbrake on. When you are ready to pull off you put your foot gently on the footbrake then take the handbrake off. Very rarely a driver can put their foot on the gas by accident. The bus moves forward as the handbrake is taken off. The drivers reaction is to press the 'footbrake' harder which usually results in panic. You can see where this is leading.
In this case the driver appears to loose rational thought at the prospect of hitting the bus in front, steers violently to the right to avoid it then tries to steer back to the left.
After the initial error the driver just reacts to the situation until the immediate danger is reduce to a level where tyhere is enough time to rationally work that his foot is on the gas.
There have been instances where buses have travelled several hundred yards before coming to a stop after hitting buildings or other large vehicles often with the drivers foot still planted on the gas pedal. The driver has just been panicking about avoiding as many vehicles/pedestrians as possible as he can't stop due to his 'failed' brakes all the way down the road.