Green’s Dictionary of Slang

brewising the bed phr.

also bruising the bed
[supposed similarity of the mess to SE brewis, a broth made from beef and vegetables or the fat scum from the pot in which salt beef has been boiled]

fouling one’s bed.

[UK]Grose Classical Dict. of the Vulgar Tongue n.p.: Bruising, or rather brewising the bed, bewraying the bed, from Brewes or browes, otameal boiled in the pot with salt beef.