We demonstrate a new all-fiber electrically tunable modulation method which significantly reduces the response time of a Bragg grating acousto-optic modulator. A 4 cm long device is fabricated with a 1 cm grating inscribed in a suspended core fiber. An acoustic pulse train is switched out of phase along the fiber, damping unwanted natural resonant vibrations inside the grating. The device rise time is decreased from 56 to 9 µs by tuning the duty cycle of the driven electrical signal, contributing to achieve the shortest switching time of 15.6 µs. This tunable temporal response reveals unique features to change the profile of optical pulses. High pulse modulation depths are achieved employing a compact acousto-optic modulator, pointing to fast switching of all-fiber photonic devices.