Spell cartridges is a pretty good option for this class combination.
Spell Cartridges is difficult to fit into a build due to the extra feat it costs. At higher levels the fact that it uses your swift action economy is a bit of a problem, and it takes steep competition from shadowshooting weapons that don't require any feats whatsoever.
So would myserious stranger 1 x Juggler Bard 4 be any good?
Very solid approach. The one caveat is that Mysterious Stranger has no way to fix misfires quickly. Ensure you know the Mending cantrip and learn the Jury Rig spell as options to quickly deal with the inevitable misfires. However, the ability to get Cha-to-damage synergizes very well with the bard and if you want to two-weapon fight with firearms this is one of the few ways that works well out of the box.
In terms of feats you need Point Blank Shot and Precise Shot. You're an obligate ranged attacker, you can't afford to be shut down by enemies closing into melee range. After that you'll want either Arcane Strike and Spell Cartridges or Rapid Reload and Rapid Shot. Long-term you'll want all of Deadly Aim, Rapid Shot, and Two Weapon Fighting to complete the build.