"Oh yeah, I know Johnnie Bassett. We were part of that whole thing"

This quote by Eddie Floyd is most likely referring to a shared experience between him and Johnnie Bassett. It might be a musical partnership, a shared efficiency, or a task they both worked on together. It might likewise be a referral to a shared experience in their individual lives, such as a friendship or a shared event. The expression "that entire thing" implies that the experience was substantial and unforgettable to both of them. It could be a recommendation to a time when they both attained success, or a time when they both faced a hard obstacle. Whatever the experience was, it was clearly meaningful to both of them.