Triangulation using (possibly ultrasonic) microphones would be more feasible - the amplitude of the sound waves created by the bullet should dwarf anything an ultrasound sensor would be putting out. sound travels 1/2" in about 35us so that's the granularity of timing information. However I don't know if this is really feasible at all - a supersonic bullet would be easier as shock wave has well defined start. Relative sound amplitude will give some information too.
A grid of foil strips would be reliably cut by a passing bullet - but wouldn't be reusable.
An array of light beam sensors would work if they have a fast enough response