Bush is a very successful politician. Some of his success comes from the way that he disarms his enemies with his lack of arrogance.
The way I see it, Bush felt that there would be considerable benefit to leaving Democrats in some high level positions. Mineta was given Transportation. Mineta chose Magaw.
Who would have dreamed in January 2001, that the Department of Transportation would be involved in anything more critical than whether truckers are testing their tire pressures frequently enough or airlines are maintaining their schedules adequately.
The most important posts were those involving Defense, National Security, and the Attorney General.
The best outcome from this point is for the pilots to stage a 100% effective strike making it plain that they expect to be allowed to carry firearms. Congress will hurry legislation which makes the airlines and pilots solely responsible for onboard security of their airplanes. Bush will sign such legislation.
It would then be perfectly reasonable for Bush to expect and ask for Mineta's resignation for failure to anticipate the nation's security needs. There would be little need for Bush to justify losing Democrats from his administration in such a case. Bush might even be able to find a pro-gun Democrat to appoint in Mineta's place.