Is the Bitcoin Logo patented?
Most certainly not. Patents grant a time-limited monopoly on the use of a novel, publicly dislcosed invention. Even if
the concept of using logos for branding was once patentable, it no longer is, due to ample examples of "prior art."
Trademarks on the other hand, grant an indefinite monopoly on the use of distinctive marks. They are designed to reduce confusion in the marketplace, such that you know whom takes responisibility for manufacturing a product.
Copyright may also apply to the logo, but it is my understanding that it is under a relatively liberal public copyright license.