It's difficult to phrase this problem in a way that isn't tautological. If it would be stupid not to take the bus, then I guess I'd take the bus.

That said, I am pretty law-abiding by nature, and I wouldn't expect that to change much. My instinctive reaction is to suppose the person best able to drive the bus is the bus driver. I'd hesitate to assume he'd abandoned it. Ideally, I'd talk to him before he left. If he plans to get his family and some supplies, return to the bus and lead an evacuation, maybe the best thing I can do is help him carry out that plan.

If he's genuinely abandoned it, then it becomes a resource. However, I am short-sighted, so I'd probably be one of the people least able to drive safely. I'd be more likely to try it if I were alone then if I was putting other passengers at risk. I wouldn't normally drive my own car without my glasses, let alone a bus.

I'm also not very social. It sounded like you wanted to help all the other passengers reach their loved ones. I would hesitate before taking on that responsibility. I'd also hesitate before taking a bus for my own use that someone else could use to save the lives of others - I'm not actively evil. But given the choice, I'd rather strike out on my own than take charge of other people or let someone else take charge of me. Last thing I want is an argument about where to go. That's bad enough when we're discussing which pub to go to.

In a fallout situation, the bus would be a reasonable shelter. Fallout is dust that you don't want on your skin (or inside you). The bus will help to keep it off. It'd be better to get indoors, but it sounds like the bus driver hasn't invited his bus-load of passengers into his home and I'd hesitate to force myself upon his hospitality. Much here depends on the details. Generally, the profile I'd expect is a period of all-clear before the fallout arrives, followed by a period of high risk, that gradually tails off as the radioactivity decays. The nice thing about radioactivity is that the nastiest stuff also has the shortest half-life. If you can get to a better shelter in the window before the fallout arrives, that's good, otherwise waiting in the bus for, say, 2 days might be better.

I'd expect the bus to have some communications, and maybe a first aid kit and possibly other resources.