If they could have taken him out with a bullet, they would have, and no one would be questioning if they should have or not given that he was still an active threat.
The nice thing about a large explosion, though, is that most remote bombs use signalling that takes time to send. If he was using a dead man's switch method (ie, if he dies the bombs go off, usually because he lets go of a button or falls off a pressure plate or similar) then a bullet would end up triggering the claimed bomb(s).
However, a large explosion would likely damage any dead man's switch and electronics enough, and quickly enough, that a signal wouldn't be sent.
Of course a determined bomber could build a robust dead man's switch, but the vast majority of bombers use simple, improvised methods and don't go to the trouble of a more robust method.
So an explosion might simply have been a better option for killing someone claiming to have bombs around the city they could set off remotely.