I may be wrong about this, but it seems that Bush exploited something of a loop hole, or gap, in the law and Constitution when he issued an executive order directed at firearms imported from foreign nations.
Actually, he just exploited the "sporting purpose" clause in 18 U.S.C. 925(d)(3). The ATF had made two prior rulings (94-1 & 94-2) in 1984 that the Striker-12 and Street Sweeper shotguns were not eligible for import because they were not “particularly suitable for sporting purposes.” The same study leading to that was the one that ruled police competition and practical shooting competitions didn't count.
Having seen those rulings withstand scrutiny and challenge (which was faint at best), they pressured Bush to apply the same standard to "assault rifles." At the time, the idea of banning the importation of high-capacity mags had also been bandied around, but was rejected.
In truth, there was never an EO. Bush informally directed the ATF to enforce the new interpretation.