Legends and tales of how silk began are chronicled in this very elaborate space, which houses some of the earliest known samples of silk in the world. Here you can learn how silk makes it from the worm to bathrobe. They've even got a large gallery of looms and several of them in use just to show how it's been done for centuries. After you're finished with the exhibits, check out the shopping area at least here you can be confident that it's the real deal. They do have tours in English.
Make a museum day of it and start with the West Lake Museum on Nanshan, down to the Silk Museum on Yuhuangshan, and then further south to the Kiln Museum on Shi Jia Shan. Easy to do if you just keep hopping on and off of bus 809.