These are popular in Germany and are available in the retail markets there. I used the Google search term "Reißverschluss Reise Bettwäsche" which roughly translates to 'bed sheets for travel that close with a zipper'. I also used "Hausstaubmilben-Allergiker" (house dust allergy) with less conclusive results.
From a canonical point of view, the objective in using these sheets is to insulate yourself from the sheets and covers provided by the hotel (or host) such that your contact is limited to your own bedding and to thereby enjoy a more hygienic sleep. They would be indispensable for tropical or dusty venues and a solid travel tip for almost anywhere else. The image below demonstrates how they work...
The red line portrays a cross-sectional view of how the sheet is meant to be used. There is a zipper on the side so that all contact with the bed and bedding is avoided.
I looked at the various offerings in the market and selected a vendor that offered the closest product to what you are looking for. I then sent them an email in German asking if they were able to handle an English speaking customer and provide this product by telephone or on-line ordering.
They answered my email promptly and confirmed they are happy to receive your English enquiries (by telephone or by email) and ship to you. The large sheet is 39 Euro plus shipping if you are outside of Germany. I forgot to ask if they will give VAT relief for non-EEA customers so it's something you can take up when you enquire.
Note for your specific requirements: this product is machine washable and tumble dried.
Their email is firstname.lastname@example.org and their site is at http://www.allergika.de/Produkte/Hausstaubmilben%20Allergie/ALLERGIKA%20Travel%20Reiseschlafsack.html
To be fair, there is another vendor at http://www.bettwaren-shop.de/ offering virtually the same product at a comparable price. There's another at vendor at http://www.allergiker-shop-alfda.de/Allergiker-Bettwaesche-Encasing/ which offers a seemingly higher quality product, including a pillow case (at substantially higher prices).