Padams, if you really want to know how they make the dye commercially, the process converts the natural dye (bixin), which is oil loving, into one that is soluble in water as a potassium or sodium salt. You take annatto seeds, grind them up, and add ethyl acetate, swirl it around and let it sit so the oils are extracted. Then you add lye (either sodium or potassium lye) and cook the whole thing in a pressure cooker. You'll get the water soluble salt this way, which you can then decant and take water out of to concentrate.
Like you already found, the easy way is to make the oil based infusion, and as you said, it doesn't work well. You'd need to do the conversion to make it a water soluble salt.