Bedford, former master distiller for Jack Daniels Distillery, died suddenly Friday at his home in Lynchburg, Tenn., the company's home base.
Details about how he died have not been disclosed.
"Lynchburg and Jack Daniel's have just always been a part of my life," Bedford, a NASCAR fan, once said. "I guess that's another thing that will never change."
Sunday, the No. 07 Chevrolet Impala SS, driven by Casey Mears, will carry a special decal with the Jack Daniel's logo, saying "In Memory of Jimmy Bedford."
Also, Kevin Harvick, Jeff Burton and Clint Bowyer will put the decal on their cars.
Bedford, 69, worked for the company more than 40 years and is one of its seven master distillers ever, a position he held from 1988-2008.