I don't wash my fabrics before cutting but I do starch them so they're dipped into my dishpan full of starch, then run thru my wringer and hung to dry. Then I spritz them with water and press them. Normally if they're going to bleed, it will happen during my starching. Once my quilt is finished I usually put it thru the washer with a color catcher so whomever I give the quilt to won't be startled the 1st time they wash it.
Once after I washed a quilt I didn't see the red bleed onto the white so I thru it into the dryer. Thought for sure it was ruined but someone here said to put it thru the washer again with another color catcher and sure enough the red bleed came out so all was good with the world again.