The total cost of a bus is just over $100/hour (I last checked in 2019, so a bit more from inflation), and a driver directly makes around $30/hr plus benefits easially will put you over $50. Now add in all training and management that isn't directly per hour but if you didn't have a driver you wouldn't pay. You do have maintenance and fuel costs per hour, insurance and the cost of a bus. There are are a lot of "it depends" and I've never seen a formal analysis of the true costs, but to round numbers we can say half the costs are the driver and be close enough for discussion.

If we take the same $ and get rid of the drivers we can run twice as many buses and that increased service will get a lot of riders who previously thought the service was too bad. Though you will need to run the additional service for a few years before people figure out service is no longer bad and start using it.

Now we do have to assume some intelligence in bus routing. There are a lot of bad bus routes in cities that will never get more riders because of how stupid they are.

Of course you are right that politics gets in the picture. Rail gets far too much attention for projects where the lowly bus is cheaper for otherwise identical service (and where rail is needed it is often done wrong). As already pointed out unions will hate this plan and they have power to screw the rest of the population (who because they don't ride now don't think they would if this plan happened) and the environment (they care about the environment only after their own self interests.

Still the numbers work on paper: self driving buses should get a lot more riders on yoru bus system because you can afford to run more service.

Are you factoring the purchase price of the bus? I believe they cost around $1m. Then there is also having to purchase the yard space to store the bus if that isn't already available. Maintenance and cleaning and associated costs. I'm not sure how often a bus is routinely replaced with a new one.