Bard and Cleric don't really work that well together except as a one lvl dip into Cleric for armor proficiencies due to conflicting spell casting stats and delayed spell progression.
Clerics will multiclass best with Monks and Druids and even these are a dubious improvement over pure Cleric. Though there is the niche case for the Tempest Cleric 2/Storm (or Blue Draconic) Sorcerer 10 build.
Bards will want to multiclass with Warlock, Paladin, or Rogue. These can go in a ton of directions depending on what you want the build to do.