Sounds like you answered our own question, Red. Make it just like a sham, except with sides like you were covering a box pillow. Using the basinette mattress for size, cut one piece of your fabric with a seam allowance on all sides. Measure around the perimeter and cut a strip that long and wide, also adding the seam allowance.

For the back, you're going to use two seperate pieces of fabric that overlap in the center. Finish the edges that will overlap, add the seam allowances and sew it all together. I say this very casually because I know you know your way around a sewing machine and have sewn for years.

If you were just a beginner, I'd have to explain each step in more detail.

Hope this is what you have in mind and that it makes sense to you.

Well thanks for the general idea and I am a beginner LOL!
I just have one question what is the strip for?
Red

The strip would be the width of the bassinet mattress plus seam allowances and as long as the perimeter of the mattress.

Thank You!