My favorite archer build is:

Eladrin (non AL, ends with 20 DEX, 10 WIS, 20 CHA)
or 
Wood Elf (AL, ends with 20 DEX, 13 WIS, 18 CHA)

Battle Master 8 / Valor Bard 12 (6 ASI, 5 Superiority Die)
or
Battle Master 6 / Valor Bard 14 (Battle Magic, 4 Magical Secrets)

Ability Scores

STR 8
DEX 15 + 2 [Race] + 1 [Elven Accuracy] + 2 [ASI]
CON 14
INT 8

Eladrin
WIS 10
CHA 15 + 1 [Race] + 2 [ASI] + 2 [ASI]

Wood Elf
WIS 12 + 1 [Race]
CHA 14 + 2 [ASI] + 2 [ASI] + 2 [ASI, 1st build]

What makes this a good Archer:
20 DEX
Elven Accuracy + Greater Invisibility
Sharpshooter
Swift Quiver (Magical Secrets)
Action Surge
Archery Fighting Style
Maneuvers

Extra ASI (with first build, eladrin) can be used to get feats such as Inspiring Leader, Skulker, Martial Adept

Other Magical Secrets could be Find Greater Steed (flying mount), Counterspell (boosted by Jack of All Trades), Haste (when you're out of Swift Quiver slots), etc. I prefer either steed or Counterspell.

If you go Valor Bard 14, you get 2 more magical secrets and Battle Magic. This lets you cast Greater Invisibility and take a shot in the same turn. With this Magical Secrets you could take Simulacrum so that there are two of you. The downside of this route is one less ASI and one less superiority die.