I am. You should definitely be able to send messages to piece objects. That's not incompatible with the Board object having a bitboard for its internal representation of board configuration. The piece objects have contextual identity based on the board configuration. Hint: they don't have positional state.
That still doesn't tell me how you map the interface to the implementation. I need a piece of code here. You won't get away buy leaving this as an exercise to the reader.