ClearAll[BurrowWheeler, InverseBurrowWheeler]
BurrowWheeler[sin_String, {bdelim_, edelim_}] := Module[{s},
  s = Characters[bdelim <> sin <> edelim];
  s = RotateLeft[s, #] & /@ Range[Length[s]];
  StringJoin[LexicographicSort[s][[All, -1]]]
  ]
InverseBurrowWheeler[sin_String, {bdelim_, edelim_}] := Module[{s, chars},
  chars = Characters[sin];
  s = ConstantArray[{}, Length[chars]];
  Do[
   s = LexicographicSort[MapThread[Prepend, {s, chars}]];
   ,
   {Length[chars]}
   ];
  StringTake[StringJoin[SelectFirst[s, Last /* EqualTo[edelim]]], {2, -2}]
  ]
BurrowWheeler["BANANA", {"^", "|"}]
InverseBurrowWheeler[%, {"^", "|"}]
BurrowWheeler["appellee", {"^", "|"}]
InverseBurrowWheeler[%, {"^", "|"}]
BurrowWheeler["dogwood", {"^", "|"}]
InverseBurrowWheeler[%, {"^", "|"}]