Federal Register - Bump-Stock-Type Devices. There is a lot of information in this link.
923-Page Opposition to ATF Bump-Stock Ban Filed.
I suspect the case will go all the way to the Supreme Court. Since the legislative branch of government has ceased to work, I suspect they will remain silent and not do the job they are supposed to do, which is make the laws. Which is why the courts have garnered more power than they should have.
But President Trump is certainly not doing it on his own. He is working within the Constitution. President Trump may have directed the ATF to re-examine their ruling, but that also is legal. They did and decided that bump stocks do meet the one trigger definition. Lawsuit was filed against that ATF ruling, and is now proceeding through court system.
We may not agree with the final outcome, NRA has no problem with banning bump stocks, but at least it is an orderly process. It does, however, expose the uselessness Congress has become, they no longer do their job at all. Why? Because they are afraid they will not get re-elected. Makes for a good case of term limits.
This is getting tiresome. Bumpfire stocks do not cause a firearm to fire more than one round per pull of the trigger. Each round fired is caused by a single pull of the trigger. The fact that the recoil of the firearm actuates the trigger is irrelevant to the legal definition of a machine gun. ATF rexamining their previous ruling and suddenly determining that bumpfire stocks are now machine guns is akin to John Roberts gymnastics in the Obamacare mandate ruling.