One approach to orange walls is to make everything else in the room bright white. So choose white sheets for your bed and a white bedspread or duvet cover. Make the bed itself white as well as the floor and all the other furniture, lamps and accessories. The crisp contrast between orange and bright white will make your room scintillate with a clean, modern look.
For a softer, warmer effect, complement the orange with creamy whites, browns and black and maybe accents of gold or yellow. You might choose creamy white sheets or brown ones, or select a pattern with brown, black and white. Consider also animal print sheets, such as zebra or leopard, for a safari feel. Using earth tones of brown and terracotta will fill the room with a warm glow.
You can also contrast warm orange with cool colors ranging from muted gray-blues and greens to brilliant, jazzy, apple green, cobalt or peacock. Bedsheets in gray, soft blue or gray-green would soften the brilliance of the orange while sheets in sharp green or blue would vibrate electrically against it.
Another choice is to use colors on either side of orange in the spectrum -- red or yellow, or red's lighter variant, pink. Orange/red is an active, hot combination while orange with pink is more funky and mod. Orange with yellow can be as cheerful as a lily or a sunrise. Whatever color your choose, your room can be a dazzler.