The Patent Bar Examination is one step in the process of registering to practice before the United States Patent and Trademark Office (USPTO).
In order to even apply to take the Patent Bar, you must demonstrate possession of scientific and technical training: mainly the requirement is met by either having a Bachelor's Degree in a recognized technical subject, or by providing documentation or objective evidence that otherwise qualifies the individual and satisfies the Director of the Office on Enrollment and Discipline (OED). 37 C.F.R. § 11.7(b)(i)(C).
However, you needn't have a J.D. to take the Patent Bar Examination: thus, you can take it at any time it is offered. 37 C.F.R. § 11.6(b).
The examination: