I travel with DD on the buses practically every day and have no trouble.
For babies and sleeping littl'uns, a lot of drivers will allow the buggy/pram to be in use even when the bus is full.
Just park it in the bi
g elederly/wheelchair gap and sit with them.
We tend to travel off-peak, and the drivers are absolutely fine with DD's stroller being stuck in elderly/disabled legroom-ish space near the front (brakes on!) so long as no one else is there - while DD runs up to the very back to the bus and proclaims herself queen of the castle.
Tbh we're often the only ones on the bus when we travel, but if there are more passengers I just fold the buggy up and plonk it in a storage alcove.
A lot of buses do also have the buggy/bicycle hook-up doohickeys on the front too, though I've rarely seen them in use.
More info here.
There are a few bus companies running the various routes, and I think I've travelled with all of them at one point or another.
None have given me a hard time with little one, unless she's being slow to get off or climbing all over the seats...