Good question but I think that the answer lies in two parts. First, if you'll recall, Bush #43 (W) said he would sign an assault weapons ban. He could say this and be comforted in the knowledge that Congress would never send him one. But I'm pretty sure that he would have done so had one been sent to his desk.
Part two of this lies in his daddy, Bush #41. That Bush is decidedly antigun. He's the guy who got rid of all our cheap Chinese, Egyptian, Czech and Bulgarian 7.62x39 ammo by an EO ban. He's the guy who also banned (by EO) the superb H&K PSG-1 long range rifle from ever again competing at Camp Perry or being used to take game at 800+ meters. At a minimum of $10K to buy one, it wasn't high on the list of guns wanted in da 'Hood. This was also the guy, you'll remember, who coined the term for our society just after Gulf War #1 of New World Order, in 1992. That is not an accident.
W signed everything. His veto record is appalling.