Light pulses entering an elongated bottle microresonator (BMR) from a transversely oriented input-output waveguide (microfiber) slowly propagate along the BMR length and bounce between turning points at its constricting edges. To avoid insertion losses and processing errors, a pulse should completely transfer from the waveguide into the BMR and, after being processed, completely return back into the waveguide. For this purpose, the waveguide and BMR should be impedance matched along the pulse bandwidth. Here we show how to enhance the impedance matched bandwidth by optimization of the BMR effective radius variation in a small vicinity of the input-output waveguide.