As has been indicated, different rail companies have different policies on accepting bicycles. (These are largely determined by the type of rolling stock which the company uses and also the levels of congestion on certain services).
To view the cycle policy for any rail operator, click on the link for the relevant company here:
http://www.nationalrail.co.uk/tocs_maps/tocs/
Then scroll down to 'Onboard facilities'.
There are a few buses in rural areas where you can board with a bike (or put it in a trailer behind the bus) but these probably account for well under 1% of the buses in the UK. You might also find a few drivers (once again, in rural areas) who'll 'turn a blind eye', even though they shouldn't actually let you take your bike. However, in general, it's best to assume that bikes are barred from buses.
Chris