We express the detachment cross section caused by a Gaussian pulsed laser in terms of that caused by a continuous laser. Using this expression and Poisson's summation formula, we derive a uniform semiclassical formula for the cross section of pulsed-laser photodetachment of a hydrogen ion in static parallel electric and magnetic fields. The uniform semiclassical formula does not have a divergence problem at the bifurcation points. Numerical comparisons show an excellent agreement between the uniform semiclassical formula and the quantum formula for the detachment cross section.