Not a pro on drapery but I believe felt is often used as an inner liner to do just that.

inner lining is flannel, generally.
you can use felt if you want an extra thick inner lining, but your seams will be thicker.

as for bump, i'm not sure what that is.
is it the stuff from baby blankets that people call "minky"? because that would give your linen a weird texture.

the flannel and then a regular lining to the back will be fine with the linen, it won't be too heavy. it won't flow in the wind like normal linen, though, so remember that.