So everyone is supposed to hold on to their bones after each round?
That is correct. Your supply of bones will continue to grow round after round. They are not discarded after each round. You may discard bones during a round by taking the "Donate" action, but in general your supply of bones will continue to grow.
I just got my copy of the game in and I think the rule book says to discard bones. That's why I was initialy confused regarding my initial post. I could have misread the rule book but I'm pretty sure it says to discard bones after each Exhibit Phase.
The last line in the Exhibit phase says that dinosaur "bonus cards" are discarded after scoring. I bet that's where the confusion started. After a bonus card is scored it is discarded. "Bones" remain round to round.