Bassist Oteil Burbridge didn’t know what he would do after the Allman Brothers Band, which he had been a member of for 17 years, played its final show in October, 2014. He played some one-off shows and had a brief reunion with Col. Bruce Hampton’s Aquarium Rescue Unit. Then he got a call to audition in California for Dead and Company, a new band that Grateful Dead members Bob Weir, Bill Kreutzmann and Mickey Hart were forming with singer/guitarist John Mayer and keyboardist Jeff Chimenti.

“The auditions were not at all formal,”...