No. He is an employee, and as such it is up to the company to decide what advertisements they run on the side of their bus, what livery and other decorations the bus has, and so on, not the driver.
They may choose to offer him an alternative vehicle to drive, but they are not and should not be obliged to.
I'm a bit torn on this one.
What would you say if it was instead say an advert from an atheist group saying "There's probably no god, stop worrying and enjoy your life" or perhaps "There's probably no god, stop worrying and enjoy your life" or words to that effect and a Christian or Muslim driver refused to drive the bus with that advert on?
Ditto but the atheists are more militant and now a Mohammed cartoon is involved along with a cartoon of Jesus or perhaps a political advert for the BNP?
I mean currently some muslim staff members in shops will refuse to sell alcohol at their tills or won't want to handle bacon etc.. I'm not sure to what extent their employers can take disciplinary action there should they want to vs protection of religious rights at any employment tribunal.