Here are some ideas, roughly in order from "we should definitely do this" to "this is crazy, but it would probably still reduce deaths overall when you take into account that more people would ride the bus":

• Don't require buses to stop and open their doors at railroad crossings.
• Allow the driver to start while someone is still at the front paying.
• Allow buses to drive 25mph on the shoulder of the highway in traffic jams where the main lanes are averaging below 10mph.
• Higher speed limits for buses. Lets say 15mph over.
• Leave (city) bus doors open, allow people to get on and off any time at their own risk.

Other ideas?

If we made buses more dangerous by the same percentage that motorcycles are more dangerous than cars, [2] they would still be more than twice as safe as cars.

(I wrote something similar a few years ago, focusing on cost instead of speed.)

[1] See Comparing the Fatality Risks in United States Transportation Across Modes and Over Time (2013). They find buses have a fatality rate per billion passenger miles of 0.11 while it's 7.3 for cars. (pdf)

[2] Motorcycles are 29 times more dangerous than cars, with a fatality rate per billion passenger miles of 212.