Cockney rhyming slang: bottle of beer=fear. It’s more used to describe someone failing through lack of nerve than ability: “He was going to get married, but he bottled out at the last second.” Other variants are also used: “You don’t have the bottle.” means “You lack the courage”. Of course, for the full effect you need the gottal stop: “Yeh darn 'ave the bo’ll, son”
I would dispute the “bottle of beer” (i.e. fear) derivation.
The usual expression is “He’s got a lot of bottle”, which wouldn’t make much sense as “He’s got a lot of fear”.
Cassell’s Dictionary of Slang says it is from rhyming slang, yes, but from “bottle and glass” meaning “arse”. It adds that this is a play on the earlier (18th-century) slang term “bottom”, meaning “character”. So, if you have a lot of bottle then you have a lot of arse, or a lot of bottom, meaning you have a strong character.
This link (scroll down) also backs up the “bottle and glass” explanation, with the added twist that “losing your bottle” might refer to fear-induced incontinence…
I also found this brief post on alt.usage.english.