Sauté the onions in the soup pot, along with the bay leaf, until the onions turn translucent. Add the chopped green bell pepper, diced potato, chopped asparagus (leaving out those tips you set aside), water or stock, and salt. Bring water to a boil, then lower to a simmer and cook about 10 minutes or until the potato is tender.
Remove the bay leave, and purée small batches of the soup in a blender along with batches of the soy milk. (Or, if you have one, purée the soup right in the pot with a submersible blender.) Purée until the texture is totally smooth.
Return the soup to the simmering heat and add the seasonings to taste. Throw in the the aspargus tips you set aside and cook until they just turn tender. DO NOT let the soup boil, or the soy milk will separate out and get kind of clumpy. Watch the soup and stir constantly. Lower the heat the moment you notice the soy milk starts separating. You could also steam the asparagus tips in advance.