Adjective that describes a person who urgently needs to to the toilet
"Bursting" is used colloquially and widely in the part of the UK I come from. I strongly disagree with Edwin's assertion that it is "near-childlike".
"To be desperate for"is also widely used. https://www.reddit.com/r/britishproblems/comments/aacdwa/being_desperate_for_the_toilet_after_sitting_for/ https://www.thesouthernreporter.co.uk/lifestyle/cars/drivers-risking-huge-fines-and-points-going-toilet-motorway-1422240#gsc.tab=0