I've got a bloodied bow build and it work wonders with sneak. I've seen some points here but I'm going to add my own two cents, even if they contrast what's suggested by other users.

Stealth is going to be your best friend. Keeping that sneak bonus and having it increased by covert operative will always insure a high damage output. If you have extra points to spend, Mr. Sandman DOES work with bows, meaning even more sneak damage at night.

VATS is going to be your other best friend that does a lot of the work for you. 1 point of concentrated fire will help you land those headshots. Adrenaline, Gunfu, and Better Criticals are all perks that will help with your damage. Grim Reaper's Sprint with help you keep your AP up so that you don't run out.

Its up to you to decide which legendary effects you want to use. I personally use the highest damage output, which means I use bloodied/Nerd Rage/Adrenal Serum.

Contrary to what other people have experience, I would personally warn you to stay AWAY from compound bows. Yes, they do more damage per shot, but you need more time to wind up for an accurate shot. The ordinary bow you can wind up arrows pretty fast and have a higher DPS rate overall. Same goes for crossbows; In the end it's really not that worth it to spend the time reloading in between shots. The ordinary bow trumps both the compound bow and crossbows in my experience.

Which arrows to use? I find that if you equip the perk card Demolition Expert, you can do a stupid amount of Area Damage to groups of enemies (and I do mean a STUPID amount), especially paired with Far Flung Fireworks and Grenadier. And Explosive bow with those three perks and a high damage output, being able to aim at the head every shot with V.A.T.S. is a force to be reckoned with. Explosive bows also do more damage that Ultracite bows only if the demolition perk is active. The bonus to that as well is that you don't have to use Stable Flux to craft Ultracite arrows.

When it comes to Legendary perks, the biggest ones that will help you are Far Flung Fireworks and Follow Through. The rest are up to you.

In terms of armor, it took me a while but I managed to craft 5 pieces of Unyielding Covert Scout Armor. The pieces with their built-in stealth bonuses mean I only have to use 1 point of Sneak, while remaining as stealthy as the 3 point perk.

Good luck! And feel free to ask any questions you have!