XGtE Page 5
Certain game features let you take a special action, called a reaction, in response to some event. Making opportunity attacks and casting the shield spell are two typical uses of reactions. If you're unsure when a reaction occurs in relation to its trigger, here's the rule: the reaction happens after its trigger completes, unless the description of the reaction explicitly says otherwise.
"If you're unsure..." What's to be unsure about? "I ready the bead of force to drop it if the dragon takes a big inhale," is pretty clear. Especially because the character is giving up their normal action for the defense. If the dragon doesn't breathe this round, they stand around picking their nose.