If a driver turned a bike away when the wheelchair/bike bay was empty without other good reason for us they wouldn't be driving our RRS again. Internal CCTV is a wonderful thing to require of bus providers, microphones even better.
Whilst publically we have to say 'no bikes' or other TOCs get upset, policy is to take them unless absolutely not possible (ie a wheelchair in the bay)
Different area, different rules. The instructions issued by some TOCs say cycles must not be carried. I've seen people wanting a replacement bus having to make use of cycle parking facilities at the request of supervising TOC staff. Trains have dedicated areas for cycles, as well as clips or some mechanism for securing the bike.
National Rail has a clear stance on the matter - I'm sure it's not just for the purpose of inconveniencing cyclists either.
Unsecured, the bike can end up damaged, rolling out of place or injuring passengers. I'd never carry a cycle on a bus if it blocked the gangway or any of the exits, or there was any risk of it moving and doing so once on the move. Safety comes first. People are welcome to detach the wheels and stow in a safe place however.
Out of interest, which buses have a bay acting as a shared space for cycles and wheelchairs? I don't know much about PSVs outside of London's service buses but as I say, I'm learning new things in this thread.