In the narration,
Michael says there are only handfuls of all size rounds (11-1, 12:45).
Burt had options to take a single shot. Burt also mentions just before this moment for Michael to find his rounds for
Shirley, implying (weakly I'll grant you) that was not what he just fired.
Regardless, listen to the sound effects of Burt shooting TOWTM. After the shot, you hear him pull the bolt back and release the empty shell casing. (11-1, 11:10) That doesn't happen with a desert eagle which expels the casing in the same motion as the weapon being fired. If Burt had used Shirley, we would hear the shot and the shell casing bouncing around almost instantly. But instead we hear shot, silence, impact and groan, compliment on the shot, then the bolt action of a rifle and the shell casing hitting the ground.