Cut two ovals the size you want the bottom of your bed to be. I used blue fleece and orange and blue cotton print.
Cut out two strips of fabric long enough to go around the outside of your ovals and as wide as you want the bed to be tall. I cut the fleece double the width so I could fold it in half and make the sides more sturdy. Adding a layer of batting or interfacing would do the same thing. I cut two strips of each fabric.
Cut a long strip for your handles. Fold it right sides together and stitch, then turn right side out. Cut it in half so you have two handles.
Sew the two strips together so that you have an oval.
Right sides together, pin the oval strip to your oval bottom and sew it on.
Do the same with your other fabric. This will be your lining.
Put your lining inside the outer part of your bed, wrong sides together.
Iron the top 1/4 inch of your outside fabric down. If you didn't fold your lining fabric in half, you should fold that and iron it down as well.
Pin the top of the lining to the top of the outside fabric all around your bed. If you folded your lining fabric in half, you'll need to fold down the seam as shown to hide it inside the bed.
Pin it so that the seam is enclosed.
Pin your handles in between the lining and the outer fabric where you want them to go. Sew all around the top of your bed and you're done!
Make a nice quilt to go with it.
There it is. You're done!