You are not being bayesian enough.

You need the probability someone is telling the truth given the evidence of being dumb enough to say "I've got a bomb".

If the Hypothesis is 'got a bomb' and the Evidence is 'said bomb', here are my estimates:

p(E) = 10**-7 proportion of travellers who are dumb enough to say bomb (one in ten million)

p(H) = 10**-13 proportion of travellers who have had a bomb so far (one in ten million million)

p(E|H) = well, ZERO so far, but let's say 10**-3 bombers who mention the word bomb (one in a thousand)

Then p(H|E) = proportion of people who say bomb who have a bomb = P(H) * P(E|H) / P(E) = 10**(-13-3+7) = 10**-9

One in one billion people who mention the word bomb will have a bomb.

So if we close the airport each time for two hours, our losses for an actual bomb need to exceed the damages for closing an airport for two billion hours before it is worth it. That's over 200,000 lifetimes of waiting in the departure lounge.

Just.

Any comments on my maths / approach happily received.