I don't mean to depress anyone, but how would this work when the bag's owner
can set off his or her bomb at will?

The first bomb-carrier to be stopped will pull their pin immediately,
killing both the security/police wallahs and possibly many more. After that
those duties won't see either volunteers or conscientious up-close
bag-checking.

Or are we suddenly going to discover a new race of nerveless heroes who
don't mind being blown up?

It doesn't have to be in a bag. It could be on their person, or in a flask
or soft toy. The important thing is that if discovered they set the damn
thing off, which is what we _don't_ want.
There's no precaution that will serve.
If we stopped them making their grand explosive gestures they could even
start planting poison in supermarkets; that could kill hundreds more.
If this is a cultural war, they might switch to cultural targets; we could
lose the British Museum or Westminster Abbey to a feat of arson, or bombs
could go off at Glyndebourne. The LSO could be strafed with gunfire in the
middle of a concert.

There's no solution to the dedicated suicide agent.
We're in real trouble this time.

jP.