If you are looking to get the most out of your multi Rogue 2 (Cunning Action) doesn’t do much for Bard as they already have a lot going on with their Bonus Action. Rogue 1 (Expertise) or Thief Rogue 3 (Second Bonus Action) would be more optimal if you really want to focus as a Skill Monkey. The down side of the later is the loss of Magical Secrets.
That said Warlock 2 would probably be just as good, if not better, than either of those depending on which invocations you choose. Agonizing Blast would be a given, but Beguiling Influence, Mask of Many Faces, and Beast Speech would all be strong contenders for the second.
One final thing to note for your Expertise selections, since tool proficiencies haven’t been implemented Sleight of Hand covers Lockpicking and Trap Disarming in addition to Pickpocketing making it one of the best choices.
Edit: For my first run I’m torn between Ancients Paladin 6/Archfey Bladelock 6 and Gloomstalker Ranger 5/Thief Rogue 3/Spores Druid 4.
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.