In this context bottle is probably the informal BrE term for 'nerve' or 'courage'. To say that someone has "more bottle than a milkman" is a jocular way of saying that he is very bold: a milkman, who delivers milk to homes, of course has a lot of bottles.

In this context bottle is probably the informal BrE term for 'nerve' or 'courage'.

British informal mass noun The courage or confidence needed to do something difficult or dangerous.

’I lost my bottle completely and ran’

_{ODO, sense 2.}

To say that someone has "more bottle than a milkman" is a jocular way of saying that he is very bold: a milkman, who delivers milk to homes, of course has a lot of bottles.