Green’s Dictionary of Slang

bath bun n.

[rhy. sl.]

1. a son.

[UK]J. Franklyn Dict. of Rhy. Sl. 37/1: bath bun Son. 20 C. Cockney. A poor and pointless specimen, hence seldom used.
[UK]S.T. Kendall Up the Frog.
[UK]Barltrop & Wolveridge Muvver Tongue 64: ‘Come back with your hair on, you bald-headed bathbun.’ However, a lot of Cockney kids who sang that were of Irish descent. ‘Bathbun’ was a way of not-quite saying ‘bastard’.
[UK]R. Puxley Cockney Rabbit.
[UK]B. Kirkpatrick Wicked Cockney Rhy. Sl.

2. the sun.

[UK]‘Jack Jones’ Rhyming Cockney Sl.
[UK]R. Puxley Cockney Rabbit.
[UK]M. Coles More Bible in Cockney 27: The lemon is coming when I will make the Bath bun go down in the middle of the blinkin’ day.