Little Red Riding Hood is depicted as a typical 1940s teen-aged girl, a "bobby soxer" with an extremely loud and grating voice (inspired by screen and radio comedienne Cass Daley, provided by Bea Benaderet). After she sings "The Five O'Clock Whistle" in the opening to establish this fact, Bugs pops out of her basket to ask where she's going. She replies that she's going to "bring a little bunny rabbit to my grandma's. Ta HAVE, see?"
With this part of the story set up, the wolf is now introduced. The wolf switches a "Shortcut to Grandma's" sign, so that Red has to go through a long mountain path, while the wolf uses the real shortcut - a few short steps to the house. Seeing a note on the door that Grandma isn't home (apparently a "Rosie the Riveter" type who's working the "swing shift" at Lockheed), the wolf sneaks inside and dresses like grandma - only to find that a bunch of other wolves are similarly dressed and waiting in the bed for Red! The wolf (voiced by Billy Bletcher) growls for the others to "take a powder - this is MY racket!" Once in bed, the wolf waits for Red to come to the door. But in a twist, the wolf isn't interested in eating Red, but rather the rabbit she brought with her.
The wolf quickly shuffles Red out the door and tries looking for Bugs. Bugs, however, gets the better of the wolf and runs around the house, being 'chased' by the wolf. The wolf, however, is constantly interrupted by Red, who continues asking the questions from the story, such as "That's an awfully big nose for you - ta HAVE."
Towards the end of the cartoon, after eluding the wolf by distracting him into singing, "Put On Your Old Gray Bonnet (With the Blue Ribbons on It)", Bugs manages to get a glowing coal from the fireplace and sends the wolf to the ceiling by scorching his backside. When the wolf comes down, Bugs has a large shovelful of coals waiting to scorch the wolf. However, the wolf manages to catch his feet on the ends of two benches just in time, doing the "splits", facing the camera (see photo). Instead of simply kicking one of the benches away, Bugs proceeds to dump heavy weights into the wolf's arms. After clearing out just about everything in the house, Bugs is about to apply the coup de grace on the wolf - by placing a flower on top of the mass of junk and furniture the wolf is holding - when Red comes back in, bellowing "Hey, GRANDMA!" (Since Red has by now already questioned the wolf on his big eyes, big nose, big ears, and sharp teeth, one wonders what she was planning to ask next.)
By this time, even Bugs has had enough of Red's interruptions, prompting him to say, "I'll do it, but I'll probably hate myself in the morning." He descends the ladder, out of frame, there's a shuffling of the furniture... and now RED is the one desperately trying to avoid getting scorched (doing the "splits" in her dress, but modestly facing away from the camera), while Bugs and the wolf, arms around each others' shoulders, share a carrot and self-satisfied looks, and await the inevitable.