I agree with Bellaboo - too low, and also too squishy. There was another thread here recently where someone was unhappy with her cutting results and thought it was her rotary cutter, but really the issue was that she was using her ironing board under her cutting mat. You could get a large piece of plywood or something similar to set on the bed, but you will still run into the height issue.
Your kitchen counter is probably your best bet. It's a hard surface and the correct height, you won't have an aching back.