Dies to Removal

I'm a little confused as to how the Tribute trigger works on Oracle of Bones. When he ETB and they don't pay the tribute, does his ensuing ability put a new trigger on the stack?

For example, let's say I have 2 cards in my hand, Oracle of Bones and Inspiration, as well as 8 land in play. I cast the minotaur, and it resolves normally; if my opponent doesn't pay the Tribute, does that create a stack ability that must itself resolve (in which case I can cast the Inspiration in response in the hopes of getting something better to cast for free) or does is my window to cast a spell for free from my hand all handled in the resolution of the Tribute trigger itself (in which case my only choice is to cast the Inspiration for free)?

Oracle of Bones' Tribute ETB ability goes on the stack immediately after he resolves. It's not part of the resolution of the creature spell.

This happens because Tribute is worded with "as this creature enters the battlefield..." in the same way as Unleash from RTR. Your opponent makes the Tribute decision after the spell has resolved, but before the creature enters the battlefield.

TL; DR - You have priority and can respond to the trigger by casting Inspiration to fill up your hand.

Thanks for the quick and informative response, Hammy! I kind of hoped that was how it worked, but the When-If clause got me... silly Magic wordings.