I've always read the British expression as "bottom," which I assumed was a reference to the good, proper riding of a horse, sort of like having "a good seat."
You may be right about that, but here's a few from a Brit website including "bottle":
Slang Words
Below are a few slang words commonly used in Britain.
Bloke - man.
'John is a nice bloke to know.'
Botched - poor quality repairs.
'He made a botched job of fixing the television.'
Bottle - courage.
'He doesn't have the bottle to ask her.'
Cheesed Off - fed up
Chuck it down - to rain, often heavily.
'It is going to chuck it down soon.'
Chuffed - If you are chuffed, you are happy with something.
'I was chuffed to win a medal!'