Rick O'Shea, the Pinball Wizard (well, bard, but they're still magical)

This built is based off of two things, getting access to a rare item, Two Birds Sling and your DM ruling that a sling bullet pouch counts as a quiver for the Swift Quiver Spell.

The two birds sling lets you ricochet your sling attacks to a single target within 10 feet of your initial target when you hit them with an attack. Swift Quiver lets you make 2 additional ranged attacks as a bonus action.

Therefore, if there are two enemies within 10 feet of each other (say in a tunnel, or just traveling together) you can essentially make 8 attacks per round (after you get swift quiver up and running).

Multiple ways to build this, but here's the pure bard version, so you can also have a rocking sound track.

Race: Lightfoot Halfling - +2 Dex, +1 Charisma, reroll 1's, good at hiding, halflings and slings go together.

Point Buy Stats: 8 Strength, 15 dex, 15 con, 8 int, 12 will, 13 cha

Class: Valor Bard Level 10 - The main two reasons we go this route are for the extra attack at level 6, and the magical secrets at level 10. For magical secrets, we will be taking Swift Quiver and you get one other choice....thematically, I like the idea of Steel Wind Strike as a melee version of pinballing around.

We also get medium armor and the rest of the traditional bard stuff.

Feats: We have 2 feats by level 10, I'd take:

Crusher - lets you move someone 5 feet once per turn, and if you crit, the rest of the attacks against that creature have advantage until the start of your next turn...also rounds out our con stat. The idea here is that they are 15 feet away from each other, the first shot scooches them into range, and then the next 3 attacks get to double up.

War Caster - concentration checks are important

if I had a third feat, or if you prefer them, other possibilities are - Fighting Initiate choosing Archery (+2 to hit!), Sharpshooter (for when you get advantage) or Resilient - Con (again, concentration checks)

and that is the core of the build, the rest of which preference and flavor.

If going farther than level 10, there are multiple possibilities...Hexblade is probably the most attractive for multiclassing, though pure bard is also fine. if getting extra attack from another source, maybe choose College of Lore or College of Whispers for your bard subclass.

Another spell you could use at higher levels would be Tenser's Transformation...its just a shame that you can't use both it and swift quiver at the same time.

Finally, if there were a way for wizard to get Swift Quiver, I'd do Blade Singer instead.

Please let me know if you can think of any ways to improve on this