Emily Brings home a bottle with some bits of wood in it. Professor Yaffle tells them it is a ship-in-a-bottle. Bagpuss finds this puzzling, wondering where it would sail to. With the help of a nursery rhyme and a poem about Mermaids, the ship is magically reassembled.
Emily brings in a very old, very dirty dirty bit of rag, which Yaffle can see no value in (as ever), the mice start to vigourously clean the cloth before being stopped by Madeleine. She implores the mice to be more gentle with the cloth, and they clean it lovingly, to reveal an old cushion cover with an owl on it. The mice run away, scared by the owl, but come back when they realise it isn't real..
Emily brings a collection of ornamental enamel pieces. For a while these are a cat and a bird, but later they decide that it is a necklace of jewels for a frog princess who doesn't fancy any of the young princess, so she kisses a frog and becomes a frog princess and lives happily ever after.
One dirty old shoe is left for Bagpuss & Co to repair, and the mice suggest that it might be suitable for living in, which leads Madeleine to sing along with the Mouse Organ. Yaffle doesn't beleive anyone could live in a shoe, so the mice trick him by going round and round and appearing out of the shoe.
Nobody really knows what the floppy tartan cloth object that Emily has brought is, except Bagpuss. He says it is a small soft Hamish, a Highland beast that keeps its distance because it makes a terrible noise, like bagpipes being played bagpipes (it is bagpipes being played backwards). He tells a heartrending story of Tavish McTavish, who also made a terrible noise playing his bagpipes forwards, and his friendship with the Hamish
Emily brings some broken pieces of what seem to be Ivory. They fit together into a nodding Chinaman. Professor Yaffle tells the story of the wise man of Ling-Po who just wanted to be left to live in peace on his island and talk to his friends the turtles. But the local people like turtle soup and come and catch the turtles. The wise man asks them not to, but they laugh at him. So, he walks across the wooden bridge from the island to the land, breaking it down as he goes. Now the people laugh at him even more, saying he is a stupid man because he cannot return to his island. The wise man tells them not to be so silly, and walks briskly back to his island across the water
The thing that Emily has brought is obviously a tatty straw elephant without any ears. They try to solve the mystery of how it lost its ears by singing songs, some of which are rather painful, but finally the ears are recreated.
Emily leaves a box in front of Bagpuss. A box with windows and a front door. The mice open up the box to reveal the Marvellous Mechanical Mouse Mill. Gabriel and Madeleine then sing a song about milling with help from the Mouse Organ.
This is a heap of pieces, probably of a Staffordshire figurine. It is also said to be a statue of a giant, but if so, it must be the smallest giant in the world. A story is told about Mrs Smithers-Rowbottom who has a magic ubrella which glues things together. This repairs the statue, but the mice dispute its size, so Madeleine sings them a song about comparative sizes.
Emily brings in a bunch of tangled cottony plant. it is Old Man's Beard. Why is it Old Man's Beard? Bagpuss tells them the story of the king who had a marvellously silver beard which would make rich carpets, and of the other old men who wanted to sell their beards to the carpet-makers, so they cut them off and washed them and hung them in the hedges to dry, but none of them were as silvery as a truly royal beard. Madeleine sings the song of the master-weaver, and Charliemouse is fascinated by the art of weaving and demonstrates it to Bagpuss by himself being the shuttle.
This is an old bucket upside-down, with holes in it. Smoke is coming from it. The mice run to fetch water but the sound of Irish fiddle-playing is coming from it. Gabriel recognises it as being played by a leprechaun and he tells a story about a leprechaun and some cabbages. Madeleine sings a song about Brian O'Lynn. In the end the mice tip the bucket over, but there is no leprechaun in it, only a tiny fiddle. Charliemouse picks it up and plays it marvellously. He explains that he isn't playing the violin. It is playing him.
Yaffle comes down from his bookend to find a basket with things in it. The mice search the basket and find a twig broom, which leads Madeleine and Gabriel to sing the song about the woman who brushes the cobwebs out of the sky.
Emily brings in a piece of cloth, which Charliemouse identifies as a house for a rag doll, which leads to a number of rag jokes from the mice. The mice fold up the cloth so that bagpuss can use it as a thinking cap, and think of the story of Uncle Feedle. Gabriel and Madeleine sing along.