Why would Bush support anyone that didn't line up with his beliefs? The question then is: Does Bush support gun control?
I bet that the answer is, "Yes"! Bush has always been in favor of the AW ban; his campaign website in 2000 made no bones about it at all. Yet, he signed shall issue CCW legislation as Governor of Texas. I think Bush is in favor of "some gun control" and would not hesitate to sign any and all laws that Congress forwarded to him. After all ,he has nothing to lose by doing so. Bush is also a shrewd politician.
My support for him (and the Repubo Party) in the last election hinged almost totally on the successful sunsetting of the 1994 AW ban. Yet, he did not actually say anything other than that he was in favor of AW bans; the Republican Congress let him off the hook by not bringing the McCarthy bill forward for a vote. In the House it would surely have been defeated. But nothing is a sure thing when dealing with politicians whose job descriptions begin with the statement, "Must be a consummate liar."