I order online from the Fabric Depot in Portland, OR. fabricdepot.com
They carry Kona Cotton which is one of the best cottons in white that I have found. It is not so thin that it will show thru and it is not so thick that it is not easy to work with. It has a good weave and is relatively inexpensive. In fact, whenever I have the need for a solid fabric I shop Fabric Depot online before I look anywhere else. Their service is fast and they have quite a large selection.
Gitlisgal
Oregon