What is the thin fabric that covers the bottom of box springs called?
Where can it be purchased online?

This may be helpful:

"Cambrick
Non-woven cloth that covers the bottom of the box spring unit. Also
called a dust cover."

http://www.verlo.com/learningcenter/glossary.jsp

"dust cover 
An inexpensive spun or plain woven fabric that covers the bottom of
upholstered furniture or box springs.  Originally made of
non-colorfast cotton fabric, most of today?s dust covers are made of
spun polypropylene."

http://www.carpetbuyershandbook.com/carpet_glossary_d.htm

http://www.perfectfit.com/products/shopdisplayproducts.asp?id=6&cat=Furniture+Base+Fabrics

"Dust Cover 

Tricon - Our 100% polyester spunbonded nonwoven is our most widely
used dust cover fabric. Tricon's superior strength and coverage
combined with its value will help you eliminate costly repairs due to
dust cover tears and punctures. Tricon is available in gray or black
in both 2oz and 3.2oz constructions.

Accord - This spunbonded polypropylene nonwoven fabric is widely used
as a dust cover or cambric due to its excellent coverage and soft
hand. Accord is the recommended dust cover for those manufacturers
using a solid or webbed base. Accord is available in a black color in
weights of 1.25oz, 1.5oz, 2oz, and 2.5oz per square yard. Accord is
available in your desired widths.

Duotex - This needlepunched nonwoven polypropylene fabric is an
excellent choice for dust cover. Duotex offers good coverage, high
strength, and excellent tailoring for this application. Duotex is
available in weights of 2.3oz, 2.7oz, and 3.1oz per square yard.
Colors include black, gray, tan, and white."
 
http://www.hickorysprings.com/products/constructionfabrics.html

Thanks for the help!