Anna Maria Horner, clever woman that she is, has started selling continuous bias-cut binding. Right now, she just has a few prints available, the XOXO and Stockings prints from Loulouthi (both of which make excellent bindings).
It doesn't seem to be widely available. AMH has it for sale on her own web site in 12-yard rolls, and you can also buy it by the yard from Fabric.com. If you know of any other sources, feel free to post them in the comments.
The binding comes in two widths--2 1/4 inches and 1 1/8 inches. Note: This is the measurement after the fabric has been folded in half. The 2 1/4-inch binding is a piece of 4 1/2 fabric folded in half, and the 1 1/8-inch binding is a 2 1/4-inch piece of fabric folded in half. For binding a quilt, you'll want the 1 1/8-inch size (on Fabric.com, it's 98 cents/yard).
I know, because I bought the 2 1/4-inch size. It worked out fine, because I just cut it down the middle. That took away some of the convenience factor, but it gave me 20 yards of binding for about $15, which seems fairly reasonable. It felt like a frivolous purchase (I really don't mind making binding...although bias binding isn't my favorite), but it really is quite a bit of binding for the money.
(Sorry if this sounds kind of like an ad--it isn't! Just my personal opinion. And in my personal opinion, everything AMH does rocks, so I might be a bit biased. Ha! Biased! Get it? Sorry about that too.)
I hope that answers your questions! If you have any others, let me know and I'll try to answer them.