My friend used one of these. From memory she used a fitted cot sheet over it. It wasn't a tight fit but did the job ok.

I had Angus in his cot from 4 weeks, he didn't like the bassinet in our room. I just tucked him in nice and tight. I had a woolen underlay under the sheet and he was also in a sleeping bag, but he was born in June so it was chilly.