how does the accounting work out for the driver's health care and retirement pension?

a typical California city must contribute quite a significant sum so that the bus driver can retire at, say, 70% of their highest salary level. (e.g. over the past year, about 20% of Los Angeles's budget went to paying for the retirement of past employees.)

how does Germany do it?

The employer pays 9% of the monthly wage directly into the federal pension insurance, 7% directly into the federal health insurance. Roughly 1.5% into unemployment insurance

The rest is handled by the employee.

Pensions are paid by the employees pension insurance, and the federal pension insurance, not by the employer.

Note that this is different for certain kinds of civil servants (so-called Beamte). A rule-of-thumb for a typical public entity is that about 10% of the budget go to health and pensions of those public servants (but the exact number varies substantially between different entities), with rising numbers.

There was a distant time where some bus drivers were also appointed Beamte but that practice was done away decades ago, so there are only very few such drivers left.