If you can get yourself to Burgos, there is a Decathlon store then and you can pick up a bike off the shelf there. When you get to SdC, Correos next to the cathedral will send it back to Switzerland for about €100.
Alternatively you can contact Bicigrinos or BikeIberia who can rent one for between €200 - 300 depending on the length of time.
I've done this - picking up a Decathlon bike in Logrono - and found it more convenient than hiring, but it depends on whether you intend to keep the bike later.
As regards the rental option, I can't say as I have not done it, but I know BikeIberia have English speaking staff. Try their cell on +351 96 963 0369
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The number for Bicigrinos is on their site
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