I make my own sushi ginger using regular ginger root (the funny tree-shaped
pieces of ginger sold in the grocery). Try to shop where the ginger is
fresh, as it will be more tender. Some places to try are an Asian
market, natural food store, farmer's market or a higher end market. My
local grocery store has a fast turnover, so theirs is actually quite
fresh and tender.
Wash, peel, and slice. Place in a glass jar of white or pink wine, cider
vinegar, wine vinegar, or any lightly flavored vinegar. Cover and let it
marinate at least several days in the fridge and you have mild tasting,
pickled pink ginger. Keep refrigerated and it should last several months.
I don't even slice it into sushi-size pieces until I'm ready to use it.