It's an extension of rhyming slang.' Bottle and glass : arse. Someone who is in great fear, panicking, defecates, they 'sh1t themselves'. So someone who has lost their nerve is said to have lost their 'bottle'.
I've also heard older Cockneys say that it is a rhyme for "class" as in "style," "standing" or "reputation".
The word "Aris" or "Arris" is a rhyme for "arse" as in
Aris = Aristotle = bottle = bottle & glass = arse.