I do not think the kind you describe is bottomless. It is kind of like a drawstring purse with slits so the spout and the handles stick out for easy pouring and a cool-to-the- touch handle. You open the draw strings, set the pot into the cozy, and draw the string tight. I suggest you make yours really thick for better insulation, maybe even using two strands of worsted together. I would think it would be quite easy to make your own pattern.

I use a small two cup teapot, and I made a tea cozy from 1/4 yard of doubled over quilted cotton. I just hand sewed a square envelope type edged cozy and left the bottom open. I slide it over my teapot and it works well. I tell myself that if I want to embellish it, I should pick a color of the print and make tassels for the top two corners. This cozy works really well.

here's a place to start looking - some of the links are not active but there are a few that have pictures - the fox-glove and teapot cozy both have patterns/pictures

Here is a link that might be useful: Crocheted Teapot and other cozy links

Susan, that foxglove cozy looks cute. I may have to give it a try. Thanks