"Reflecting" addition
I don't think your code agrees with your spec: Your code looks like it can only implement a function built from three line segments.

You shouldn't need explicit resize.

bounce (lo, hi) x dx = let
  (bounces, remainder) = divMod (add dx $ x-lo) $ hi-lo
  in (if even bounces then lo + remainder else hi - remainder
     ,bounces /= 0)