Getting hit makes you bloody, but that's not the end of the story. When a hero gets knocked down, he gets back up, and in this game you're playing a hero. It's right there in the title. This is handled through recovery.
Recovery is something that happens at the top of every exchange before anyone bids any points. Before anyone does anything else, they convert a number of bloodied points to bruised points. Then the exchange progresses as normal. What are bruised points? They're normal Hope and Destiny points that can't take any more damage. So you can still bid then to generate effort, but they're still useless in terms of taking additional hits.
Notice I said recovery takes place before each exchange. That's because recovery isn't healing so much as it is rallying your reserves and getting your fight back after taking a shot, or a most palpable hit if you're feeling more poetic. That cut isn't magically closing up, but the initial shock and pain that took a big chunk out of your ability to act is being worn down by your irresistible heroism. You'll still need that looked at, but as far as this conflict is concerned it's only going to be in the way for so long. Adrenaline and pressing need can keep you on your feet until your entire Pool is bloodied and bruised.
So what about in the calm spaces? Conflict resolves and the game returns to narrative time not broken in exchanges. Can you ignore the damage or at least go straight to bruised? As it turns out, no. If you end a conflict with bloodied points, they stay bloodied. Without that moment of crisis to push you on injuries, and their debilitating effects, have the luxury of lingering. If, however, you enter into another conflict with bloodied points in your pool, you can begin converting them to bruised points right away. The conflict's back, and so's that pressing need in which heroes thrive.