Of course they should have used the army. But do a little digging on them in the meantime. (A throwaway line about following the money trail could have helped, even if Palpatine has the equivalent of a Swiss bank account.) The bomb won’t go off if you safely remove the fuse.
There’s just too much plot convenience playhouse going on that benefits the bad guys. Nobody ever pays Palpatine a visit when he’s got the black hood on and making a long distance call. (Would be really funny if he was addressing his minions from a locked bathroom.) Is there a Sith lord in the house? Who knows, our ability to use the Force is diminished. (Yet Yoda can sense Anakin opening a can of Dark Side on the Sandpeople light years away.) Dooku can’t possibly be behind the attempts to kill Padme, it’s not in his nature. Oh wait! He’s evil now!
One of the funniest bits in Frink’s AOTC edit is Mace and Yoda contradicting themselves on the “Who authorized the clone army?” thing. Cracks me up every time. 😉