Bard's passive allows for an AOE cone shaped damage thing, scaling off AP and is also affected by his AD. With AD and attack speed, Bard's DPS is amazing, and can also support the ADC with heals and Poke (strong poke)
As you collect meeps, your passive gets stronger with your AOE cone shape damage coming up more often and has more damage. You deal 2 types of damage - AP and AD. This makes it difficult for enemies stacking only armor or MR.
Overall, bard has a lot of utility build in and can also burst down targets quickly with meeps.

Spellthief's Edge
Each meep hitting a champion counts as a stack for spellthief's edge, so this helps bard earn lots of gold quickly. Frost Queen's Claim also provides bard with a slow CC and some AP.
Blade of the Ruined King
This gives bard a lot of attack speed, some life steal and some attack damage, as well as a slow that combined with Frost Queen's Claim, can slow any champion into submission.
Mobility Boots
This gives bard the ability to roam freely and collect charms and be back in lane in a flash.
Trinity Force
This gives bard a little bit of everything: Health, mana, critical strike, spellblade etc etc
Zephyr
This item gives bard more AD and Attack speed, together with some cooldown reduction, tenacity and movespeed. This helps bard roam better and hurt more in fights. Recommended as 3rd or 4th item.
Last Item
Infinity Edge - This gives bard the "oomph" he needs to dominate teamfights, with his innate utility, this item can catch anyone off guard underestimating Hybrid Bard.
Statikk Shiv - This item gives bard more roaming potential and more damage(meeps+statik) to unsuspecting targets.
Nashor's Tooth - This item allows for more burst on meeps and some cooldown reduction for more utility. Your DPS will definitely increase after buying this item. Would recommend.
Black Cleaver - This item makes you a tad bit buffer and can shred your enemies' armor for both you and your team.

Bard's scaling on his passive is insane, with at around 70 meeps is 210 (+30% of his AP), with his attack speed, his passive slow and on-hit effects from frozen mallet with allow for stickiness and allows for quick and efficient skirmishes with other ADCs or Mids.

Example of burst:
Cosmic Binding > Auto Attack (procs sheen, shreds armor, applies a slow, auto attack damage and meep damage) > Auto Attack (shreds more armor, applies a greater slow, auto attack damage and meep damage) > Auto Attack (shreds more armor, applies a greater slow, auto attack damage and meep damage) > Cosmic Binding > Caretaker's Shrine (to escape)