Your tongue will be blue for about 2 to 4 hours.
Blue tongue resolution speed will depend on how much you moved it around your mouth while it was in there.
There is no antidote but if you need to get the blue away faster, coffee and hot liquids in general seem to help.
Here are a few suggestions from Dr. Ted:
When methylene blue is reduced, it decolorizes.
Reducing agents such as sodium hydroxide — say, add 1/4 tsp baking soda in 4 fl oz water and rinse the mouth with it for a few minutes — should reduce the methylene blue.
Since the reaction is acid-catalyzed, perhaps rinsing the mouth with 1 part vinegar, 1 part water first, right before rinsing with baking soda, would hasten the decolorizing reaction.
We also find that hot liquids help as well.