Skeptoid episode #611 covers this claim and its foundation, specifically that static electricity builds up throughout the day. This is false. Fortunately, Skeptoid even covers the bedding aspect:
There is a final nail in the coffin of earthing. The entire reason for its practice claimed by its advocates — that your shoes keep you electrically insulated from Mother Earth — is false. This is why people sometimes get electrocuted: there's a conductive path from you to the ground. It's why you have to step up onto an insulated platform to make your hair fly when you touch a Van De Graaff generator in a museum. It's why people who work with high voltage have to buy special non-conductive shoes that have an "EH" rating. It's why lightning sometimes selects an unfortunate person as a conductive pathway to the ground. Normal shoes are only so-so insulators. All day, every day, almost all of us are grounded already.
This is equally true when we're lying in bed. Yes, it's likely that the feet of some beds are perfect electrical insulators, but that would be the rare exception. Bedsheets, mattresses, blankets and bed frames all have some amount of conductivity. Some textiles, in fact, are pretty good conductors — especially those made of natural fibers like cotton, wool, or silk, and even more so when the relative humidity is higher.
If this seems improbable to you — that bedsheets and mattresses and socks and running shoe soles are electrically conductive — compare them to dirt, gravel, or concrete that an earthing enthusiast walks on in his bare feet. That's certainly not highly conductive. But it doesn't have to be; all of these things only have to be conductive enough for you to be grounded. A perfect electrical insulator has infinite resistance; no electrons get through at all. But almost all materials have some conductivity, even if it's very small. Since there is always some connection between your body and the ground all day long — even through layers of fabric and carpet and shoe soles and building materials and what not — no matter how incredibly small that conductivity might be, it's still more than enough to maintain a similar charge between your body and the ground beneath you.
Fortunately, Skeptoid does include research references.