Green’s Dictionary of Slang

burst n.2

also bust
[SE burst, a sudden flurry of activity; 20C use is mainly Aus.]

[late 19C–1910s] a spree, a party with much eating and excessive drinking.

In phrases

(go) on the burst

[mid-19C–1940s] (to go) out on a spree, (to go) on a binge of food and drink.