I want to get all kinds of wool without getting the dyes to color the sheep. But what color wool do you get from sheering a rainbow sheep in bedrock edition?
The color of wool a disco sheep will drop is unaffected by its rainbow coloring. Instead, it will drop wool of its original color before the rainbow effect was added.
When shearing a jeb_ sheep, you will get the same wool as its color before it became jeb_. If it was blue before you turned it into jeb_, for example, you'd get blue wool.
As pointed out by @Egor Hans in the comments, there's an additional mechanic involved with dying jeb_ sheep - you can dye a jeb_ sheep to change its internal fur color (and thereby the wool color it produces), even though it's not visible to you due to the Easter egg override. For example, if you named a brown sheep jeb_ and applied some blue dye to it, there will be no external change visible, but the sheep now produces blue wool instead of brown.