Fundamentally battery buses are going to be cheaper to run. Regardless of initial outlay costs electricity that goes directly in with no conversion is achieving near 100% efficiency. Whereas with hydrogen that same electricity is being used to do electrolysis to get the hydrogen to begin with, compressing into fuel containers, travelling the fuel around the country and then pumping the fuel back in and then all the conversion losses from hydrogen to electricity to drive the vehicle. That chain is at best about 30% efficiency so its going to cost 3x as much at least.

While it gets you better fuel density for added vehicle complexity its pricey to run even when the infrastructure exists, which it currently doesn't. Hydrogen is notoriously difficult to store because its the smallest element in the periodic table it just wafts through whatever container we try to put it in too causing a constant loss of fuel.

There might be circumstances where its the right thing to do and the extra cost is worth it, public transport is unlikely to be that scenario. Its got value mostly for remote locations where the nearest electricity is quite far away, although the issue then becomes can you get the hydrogen there. If it never reaches proper economies of scale and infrastructure deployment it might always be a dead end and there really aren't that many people using vehicles so remote to have no access to electricity but are carrying fuel cells to get the range they need.

> same electricity is being used to do electrolysis

Nowhere in the world is electrolysis done at scale. Industrial hydrogen almost exclusively comes from steam methane reforming (SMR).