What he should have done:
Park the bus, put the 4-way flashers on, call dispatch and request immediate police assistance for an emergency (or, if he felt that would make her more hostile, push the silent alarm that is available to all bus drivers in major metro areas and leads to an immediate emergency police response). If she continued to physically assault him (which it didn't appear she was inclined to do), use necessary force to defend himself. Not verbally antagonize the passenger, not leave the seat, and most definitely not beat the shit out of her.
My answer would be the same if this person were a male, but it's worth noting that the passenger would have been a greater threat if she were male. This chick was completely obnoxious and bitchy, but unlike a lot of young men, I see no reason to think she could or would have beat the driver up or worse.
I represent both bus drivers and our local transit authority and have dealt with a number of situations in which drivers used force against people who had assaulted them, but, as in this case, pursued the assaulter rather than merely acting in self defense. The normal penalty is to fire the driver. They are entitled to grieve this including, if the union votes for it, to arbitration. If an arbitrator reinstates them, that is the arbitrator's choice and not the transit authority's. I have handled three cases like this for our transit authority. I won two and lost one.
I know this video is entertaining, and I am no fan of that young woman, but driving a bus requires drivers to deal with unpleasant and hostile people, and if they can't do so without instigating fights and beating people up, they are a liability to the transit authority and a danger to themselves and their passengers.
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