How does Beatty discover Montag's green bullet?
At the beginning of Part Three, Beatty commands Montag to burn his home and gives him a flamethrower. After Montag torches his home, Beatty tells him that he is under arrest. Beatty then explains to Montag that his wife and her friends called an alarm on him. As Beatty is speaking, Faber yells into Montag's ear to get away. Beatty then strikes Montag on his head, and the green bullet falls out of his ear onto the sidewalk. Faber's voice can faintly be heard yelling for Montag to leave as Beatty walks over and picks up the green bullet. Beatty then turns it off and puts it into his pocket. Beatty looks at Montag and tells him that he saw the green bullet in his ear when Montag tilted his head. Beatty mentions that initially, he thought it was a Seashell radio, but when Montag "turned clever" he began to wonder. Beatty then tells Montag that he will trace the green bullet back to its owner.
To answer this question, take a look at Part Three of the novel. During a confrontation between Beatty and Montag, Montag is wearing the green bullet, the two-way communication device that enables him to talk to Faber.
Beatty has no idea that Montag is wearing this device. As the confrontation intensifies, however, Beatty strikes Montag on the head, causing Montag to stumble backward and for the green bullet to fall out of his ear and onto the ground.
Beatty picks up the bullet and grins. At first, he thinks it might be a seashell radio but then he places it half into his ear and realizes that there is another person, Faber, on the other end. Beatty confiscates the device (by placing it into his pocket) and tells Montag that he will use the bullet to trace Faber's whereabouts. This threat to Faber is one of the reasons why Montag kills Beatty.