Emily brings in a bottle containing pieces of wood. Professor Yaffle says that it is a ship in a bottle, Bagpuss wonders where such a ship would sail. Bagpuss then tells a story about mermaids which magically repairs the ship.
Emily brings a very dirty old rag into the shop which Professor Yaffle can see no value to. The mice clean it and reveal a picture of an owl with the word Athens beneath it. Madeline tells the story of The Owls of Athens.
Emily brings into the shop a collection of ornamental enamel pieces. The toys think these are a cat, a mouse and a bird at first. Gabriel decides they are the necklace of a frog princess who didn't like any prince so kissed a frog.
Emily's thing is said by Bagpuss to be a Hamish, a small soft Scottish animal with a voice like Bagpipes. Yaffle and the Mice believe it to be a porcupine without quills and sing to it to encourage it to grow quills. Finally, Madeleine reveals that it is actually a pin cushion.
Bagpuss and friends are brought a small elephant, with no ears, stuffed with straw. Bagpuss explains how its ears fell off and it got stranded on a desert island and was rescued by mice who used its ears to escape the island. They decide it may never have had ears, and give it a hat to wear instead.
The mice convince Bagpuss that Emily's latest find - a model of a watermill - takes in breadcrumbs and butter beans and produces chocolate biscuits. Yaffle isn't fooled and reveals it to be a joke.
Emily brings in a plant called Old Man's Beard. The friends try to figure out why it is so called. Bagpuss tells the story of a King who used his silvery beard to make carpets. Madeline then sings a song about a master weaver.
Emily brings in an old bucket with a hole in it. It turns out that a leprechaun - an old friend of Bagpuss - lives in this bucket, and his magic fiddle plays them some tunes.
Emily brings a basket into the shop. The mice find a twig broom in it so Gabriel and Madeleine sing a song about the old woman who cleans cobwebs out of the sky. The mice then try to make a flying machine out of the basket.
Emily brings a piece of cloth in which the mice claim is a house for a rag doll. They fold the cloth so Bagpuss can wear it as a thinking cap and think up the story of Uncle Feedle. Gabriel sings a song about living on a bus.
