“If you can’t dazzle them with brilliance, baffle them with B.S. (bullshit)” has been printed on signs and T-shirts since at least the early 1970s. James Boren (1925-2010) and his spoof organization called the International Association of Professional Bureaucrats helped to popularize the jocular one-liner. The saying has been used in government, business and education.
 
“If you can’t convince, them, confuse them” is a similar saying that was popularized by U.S. President Harry S. Truman in 1948. “If you can’t dazzle them with brilliance, riddle them with bullets” is an anti-proverb that has been cited in print since at least 1999.
     
 
Google Books
When in Doubt, Mumble: A Bureaucrat’s Handbook
By James Boren
1972
Pg. 127:
A distinguished leader of an operating foundation once stated, “lf you cannot dazzle them with your brilliance, baffle them with something else.”
   
Google Books
Take One
v. 4 - 1972
Pg. 18:
If you can’t dazzle them with brilliance, baffle them with bullshit.
 
Google Books
Return to Earth
By Colonel Edwin E. “Buzz” Aldrin
New York, NY: Bantam Books
1973
Pg. 259:
There is a sign he recently made and hung in his bathroom that contains, I think, Mike’s wry comment on life. It says IF YOU CAN’T DAZZLE THEM WITH BRILLIANCE, BAFFLE THEM WITH BULLSHIT.
   
1 June 1975, Playground Daily News (Fort Walton Beach, FL), ‘Tennis Time” by Helen Allen, pg. 4B, col. 1: 
Until next Sunday remember—if you can’t dazzle them with brilliance, baffle them with junk
 
24 August 1977, El Paso (TX) Herald-Post, “Message on the Chest” by Bob McBrinn, pg. B2, col. 3:
There is a T-shirt recommended for column writers and politicians. It states simply, “If you can’t dazzle them with brillance baffle them with bull.”
 
Google News Archive
30 July 1978, Reading (PA) Eagle, “Backstairs at the White House,” pg. 47, col. 1:
Another plaque in his office reads: “if you can’t dazzle them with brilliance, then baffle them with BS.”
(The office of press secretary Jody Powell—ed.)