Soooo.....to sum up....
The bus driver is a legend and he 100% did the right thing.
Soooo.....to sum up....
I wouldn't say 100%.
He did something which wasn't part of his employment - not in his job description. That in itself isn't wrong, but it does create a starting position of acting outside of his official responsibilities.
Being a good citizen has to be tempered by official responsibilities which you're being paid to do. I don't think, for example, one of the guards outside Clarence House would be regarded as a legend who 100% did the right thing if he abandoned his post to chase down a pickpocket he'd witnessed.
OK - that's an extreme example, but it shows that the consideration does exist, to greater or lesser degrees. Lesser for a bus driver than a King's Guard,
but not zero.
The legality of his use of force is questionable. The decision by the police and/or CPS not to pursue charges would not have been because they were convinced there was no possibility of it being unreasonable and therefore unlawful, but would have involved it not being unreasonable
enough, what on balance was most in the public interest, how overstretched are the police, the prosecutors, the courts etc, and therefore what priority should it be given.
But none of that affects his employer's view on whether him fighting in the street was likely to bring the company into disrepute or not or whether he did or did not assault a passenger - different "charge", different standards, different criteria from criminal charges of assault.
And he did have a duty of care to everybody else on the bus, which he abandoned when he set off in pursuit of the robber. What if there had been a fire? What if it had been a diversion, and when he was halfway down the road a gang steamed onto the bus and relieved loads of passengers of wallets & phones? What if a drunken malodorous beggar had got on and started hassling people? What if the robber had battered him, and he didn't make it back to the bus - how long would the passengers have been stranded before the bus company found out what had happened and sent another driver or another bus? What if people missed important hospital appointments, job interviews, getting to their job on time, connections which meant they missed trains or flights and business or holiday plans scuppered?
I know your first instinct will be to dismiss all that as "Yeah, what if, what if, what if.." but think about it. His job was to deal with situations like that, and to deliver passengers to their destinations, not to chase robbers through the streets, however noble that was, but by doing that it left him unable to carry out his job properly.
So there was a disciplinary case of some sort to be answered.
Then there's the fact that he buggered off leaving the keys in the ignition and the engine running ...
So no, not 100% doing the right thing.
And did you read the report of the Employment Tribunal?