I have always assumes as vets prescribe it once a day that it would last for 24 hours - there or thereabouts. Sorry no idea how quickly it would start - complete guess like a human oral painkiller 2/3 hours??
Bute can be detected for anything up to 168 hours (7days)(data from the FEI database).
Absorption into the body does not take long 1-2 hours.This will depend on the method the bute is given. I/V takes a much shorter time.If you syringe it in ,it also takes a shorter time.