(term) is a phrase meaning that the singer has someone’s measure. Compare Baby Bonnie’s I GOT YOUR WATER ON (Gennett, recorded 1924). Compare also Sam Collins’ IT WON’T BE LONG (1927) and the Memphis Jug Band’s PAPA’S GOT YOUR BATH WATER ON and FOURTH STREET MESS AROUND (both 1930). Chris Smith dealt with the phrase in Blues & Rhythm #236.
Contrast Wanda Johnson of Belton, South Carolina who sang BATH WATER, an unrelated song, in 2015.
Compare also BOTTLE UP AND GO.