There is already a question on What is coffee bloom here, and one about why "blooming" the grounds is necessary over on seasoned advice. A currently unanswered question here is is blooming actually necessary in French Press, which an answer to that may help answer this one.
A fair amount of instructions I've seen that refer to this step instruct you to stir after adding just enough water to get all the grounds wet. However, there are accounts of people getting the same effect just stirring after all the water is added (in non-drip styles of coffee).
Is there a significant difference between blooming with some water and blooming with all? I like being able to rinse off the stirrer with the rest of the water, but I'm curious nevertheless.