Quick Answer: If it's bleeding, wash it! 2 or 3 or 4 times, repeatedly, with soap such as Ivory Soap or Woolite. Using a detergent like Tide may dissolve the indigo somewhat due to its alkalinity.

The longer answer involves chemistry and history.

The advice to set the dye with vinegar or salt is commonly heard and seems to make sense from the standpoint that indigo is mildly soluble in a reducing solution, insoluble in an oxidized state. But these approaches cannot be an issue at the point that you have an actual bleeding hakama -- the acid of the vinegar does not glue the indigo to the fabric by making it less soluble. Possibly the tradition of "vinegar to set the dye" is a holdover from dying wool, a final rinse that would be better for the wool than leaving it with any amount of alkaline soap residue.

Saltwater also has nothing to do with the chemistry of indigo dye.

Peroxide is essentially super-oxygenated water. It will certainly not dissolve the indigo (but you might keep it insoluble and all in one place so you can rip it off with sheer determination and muscle power). Will soaking the hakama in a diluted peroxide solution help "set" the dye? You might get more thoroughly oxidized indigo chunks but that will not help the problem as the dye that is coming off of your hakama is not in the hakama -- it is ON it. Think of the excess indigo as blue fuzzballs or chalk dust. Something that does not blend with the fiber itself.

I suspect that many purveyors of "genuine, natural indigo-dyed" material heap undissolved indigo onto the cloth just to give it a darker, richer color much of which is illusion and falls off later. In real life, and with a cotton hakama, it is far better to just wash the excess out before it falls out in chunks all over your mat and furniture. But why is there excess dye in the first place?

Modern methods of indigo dyeing involve a chemical reducing solution which simply cannot get the dark dark blues that the older methods did. (The thiourea dioxide chemical commonly used for reducing the indigo to make it soluble in dyeing is commonly available as "Spectralite" usually found next to the shoe polish and such in many grocery or drugstores, in fabric or craft stores. Sodium hydrosulfite may also be used and can be found commonly as "RIT Color Remover." If youre trying to clean a mat be sure to test it on a small, inconspicuous and low-stress side spot of the mat first to make sure it doesn't take everything else off too. It will certainly be safe for restoring your white cotton dogi pants.)

To dye with indigo in these modern times, you mix up a potfull of thiourea dioxide or sodium hydrosulfite and water and add indigo (natural or synthetic -- they both have the same chemical formula). The result is a pale YELLOW GREEN solution known as WHITE indigo.

You dip the cloth in the dye, pull it out, and before your very eyes it starts to change from green to blue. Why? Because the indigo is oxidizing -- reacting with the oxygen in the air -- becoming insoluble. It's delightful and magical to see.

In theory, you can dip it back in again for another coating of indigo to make the color a little darker. This is fine a few times, but very soon you have a problem. Enough thiourea dioxide or sodium hydrosulfite in the solution to reduce the indigo not only keeps the indigo in the dye-pot in solution, it also dissolves the indigo already deposited on your cloth right back out again. Consequently, you can never get the deep dark blues obtained through traditional methods.

What were the traditional methods?

A reducing environment via bacteria in a pit of aged urine and its highly fragrant biological byproducts. Very effective, but much slower -- and extremely smelly.

An old dye book mentions a dyer who had switched to the new-fangled synthetic indigo. Apparently customers would check for the authentic urine aroma to be sure they were getting the real goods, so he included a recipe using urea to provide the "authentic" smell.

However. . . at best, indigo is not very soluble. It tends to deposit on the surface of the fiber which is why blue jeans (traditionally dyed with indigo) weather and fade the way they do; the blue eventually wears away leaving the white cotton thread showing through. If you've ever read the epic "Musashi Miyamoto" you will remember that one of Otsu's odd jobs as she follows Musashi about the countryside is pounding cloth with a mallet to squoosh the indigo into the fiber.

The old method required weeks or months. Thiourea dioxide or sodium hydrosulfite dye solutions take mere minutes but because of the impossibility of obtaining dark blues with "Authentic Indigo" by modern methods, there seems to be a temptation to make the cloth look bluer than the chemistry actually allows. What to do? Simple!

Oxidize the solution in the dye-pot so it turns blue (i.e., creates blue chalk dust) and pile these onto the cloth.

This is counterproductive per effective dyeing, but useful per economics if you want a deeper blue but don't want to waste time and money doing it right. The cloth APPEARS to be bluer thanks to a powdery coating of tiny grains of oxidized indigo deposited ON the cloth. They will fall off with wear, smurfing anything they touch.

Once again, the only cure is simply to wash the garment until the excess dye is gone. If the resulting color is too pale blue for your taste, consider machine dyeing with a RIT Indigo Blue. In either case, if you end up with a blue washer, throw in a packet of RIT color remover and all will be well.

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