"counterfeit, spurious, sham," 1839, from noun (1838) meaning "counterfeit money, spurious coin," American English slang, apparently from a word applied (according to OED first in Ohio in 1827) to a counterfeiter's apparatus.

One bogus or machine impressing dies on the coin, with a number of dies, engraving tools, bank bill paper, spurious coin, &c. &c. making in all a large wagon load, was taken into possession by the attorney general of Lower Canada. [Niles' Register, Sept. 7, 1833, quoting from the Concord, New Hampshire, Statesman of Aug. 24]

Some trace this to tantrabobus, also tantrabogus, a late 18c. colloquial Vermont word for any odd-looking object (in later 19c. use "the devil"), which might be connected to tantarabobs, recorded as a Devonshire name for the devil. Others trace it to the same source as bogey (n.1). Related: Bogusly; bogusness.