The barking dog might be on the other side of a common wall between your house or apartment and your neighbor's, or the mouthy mutt could be just outside your bedroom in a neighbor's yard. Either way, it's a problem that needs modification, if not eradication.
Place your biggest furniture -- bookcases, storage units and such -- on the common wall. Books, linens and boxes of things can absorb a lot of barking. Before you move them and fill them, add sound-absorbing material, such as shag carpeting, to the backs; it won't be seen, but it will help block sound waves. Be sure the furniture doesn't touch the wall, as it will vibrate and conduct sound if it does. If you can manage to have pieces go all the way to the ceiling, so much the better.
Carpet the wall -- literally. If you can't manage heavy carpet for a large expanse, use carpet samples to create a Mondrian-inspired pattern on the wall. If you're renting, hang large sheets of sound-absorbing material, such as eggcrate, fiberglass board insulation or even multiple layers of corrugated cardboard, that you have covered in decorative fabric and framed in wood (for attaching hanging hardware) to cover as much of the barking wall as possible. This opens up unique vistas for decorating.
Build a false wall, but remember, unless you own the property, it'll have to stay if you go. Frame out a space on your side of the common wall at least one inch deep -- more is better, depending on how much space you can afford to sacrifice in your quest for quiet -- and install appropriately spaced studs. You can cover your side with half-inch drywall without adding anything to the sound-damping dead air space between, but be sure that nothing connects the two walls -- electrical cable, plumbing pipes and any other materials that touch both can transmit vibrations and therefore the sound of music ... er, barking.
Realize and accept that no room is ever going to be completely sound-proof, but outside noise can be abated.
Move your bed to an inside wall.
Use one or more of the options for inside barking to reduce sound transmission into your bedroom through the outside wall.
Hang noise-reducing drapes at the windows. These are made of a special tightly woven fabric that can reduce sound by as much as 40 percent. As an added bonus, they can also reduce light by 99 percent.