Where can I buy bedding in Los Barrios?

I think your best best is Carrefour, Leroy Merlin or Maxi Home.  They are all in the same area off exit 112.  Basic quality.  If you are looking for higher quality merchandise I would suggest Corte Ingles or Zara Home or Maison du Monde in the Marbella area.

Ikea is by far the best.  Carrefour is cheap and cheerful.  When we moved here, Conil, we had the same question.  Went to Ikea in Jerez and got everything. There one close to you in Algeciras @ Autovía del Mediterráneo, 106, Centro Comercial Puerta Europa, 11203 Algeciras, Cádiz.

I believe the Ikea in Algeciras is only a pickup point and needs to be ordered online.  The closest Ikea is in  Malaga.  If you want bedding for personal use I would not use them but if it is just for a rental property, most people furnish with Ikea as it is basic quality.  

Depends what you buy at Ikea.  If you buy the cheap stuff its not great but if you step up a bit there's some great quality stuff.

Thanks so much for all the comments. I will check them out. I have since made an order from IKEA for 100% cotton sheets, plus I went to Cortes Ingles. Thanks, I pretty much have what I was looking for.