He had been apprenticed to Richard Harrison in 1560, but that printer died about January 1563; though definitive evidence is lacking, Bynneman likely served the remainder of his apprenticeship with Reyner Wolfe.
Through the good offices of Leicester and Sir Christopher Hatton, in 1580 Bynneman obtained a privilege to print "all dictionaries in all tongues, all chronicles and histories whatsoever."
He had previously printed and published with privileges for "bookes" [i.e. proclamations] dealing with the lottery as well as a variety of works seemingly secured after Matthew Parker wrote to William Cecil in 1569 on his behalf.
In addition to printing works by noted authors such as Edmund Spenser, Gabriel Harvey, George Turberville, and others, Bynneman printed the first Welsh New Testament translated directly from Greek in 1567 for publisher Humphrey Toy, along with the first Welsh edition of the Book of Common Prayer.
Bynneman had three presses by 1583, and, as the inventory of his property shows, had a varied stock of type, including Greek and Hebrew.