Pretty much Ken and Iammeiam covered it already, but to reiterate:
Use your off GCD attacks in-between your GCDs (Blunt Arrow/Repelling Shot/Flaming Arrow, not in that order)
If there's three mobs pulled, I dot all three and single target down the first one, re-up dots (probably not needed based on dps) and single target the next down. I'm not a believer in Quick Knock as your AOE of choice, since once you hit 50, Wide Volley procs RoD for free which can proc Quick Knock for free, so you're usually better off with the 20 extra tp for Wide Volley and pray like a BLM for Procs. Re-up Invig during AoE, don't bother with Paeon unless you bottom out of TP, which shouldn't happen unless you're running with a MNK/bad AoE partner. MP is typically better spent on Foe in dungeons, or with Ballad, I guess. Depends on how bad your healer is with mp management. Paeon for allies is only useful in content like T8/10/long fights of [mostly] uninterrupted DPS.
Be sure that whenever you use Repelling Shot, do it in the most flashy way possible. You're a BRD, damn it, you have a reputation to uphold.
Do not listen to this heathen.
I'll take your spot in FCoB until you're back, no worries.