For example, Rollo is a 6th-level berserker with 2 out of 6 d12 Hit Dice remaining, a Constitution of 16, and a maximum of 65 hit points. He is Bloodied, having 13 Hit Points remaining, which is below his Bloodied threshold of 32.
Before taking a Long Rest, the party decides to risk a Short Rest first, They accomplish this and Rollo spends both his remaining Hit Dice, regaining 19 HPs. His new total is 32, so he is still Bloodied. Note, however, that there is decent chance he'd no longer be Bloodied after spending these dice, since on average he'd be just 1 point below the Bloodied threshold.
After waiting an hour (during which he takes no damage), he starts a Long Rest. At the end of which he regains all his Hit Dice and his current HP increases to 33. He chooses to expend 3 of the HD regaining 25 HPs, putting him at 58. He has 3 HD remaining for later use.