First you need to have a proper skill (hunting, archery) but I assume you already have that as you have used bow. After that you need to have enough of marksmanship skill to speed up aiming. But remember that efficient MM skill is capped by wquality of bow and arrows used. Better quality = more damage and higher MM effiency cap.
There are 3 ranged types of weapons in game:
sling
wodden bow
rangers's bow
Sling is best for starters and you need only 6 strings to make it. It's fastest to aim with and require stones to shot. You can get stone anywhere around the world.
I strongly reccomend ot use sling until you reach about 140+ MM skill. Damage is calculated by: 60 * sqrt(q of sling /10). So q300 sling has max damage around 328. Mnimum damage varies of what animal or enemy your are shotting and is affected by your perception (higher you have more damage you will make) and their agility (more they have less damage you will make). Then it is a rng calculator that calculates damage between your minimal and maximum damage.
Wodden bow is and upgrade and you need to have archery skill to use it. With wodden bow u aim 2x slower than with sling making it harder to hit some targets. So your aim bar will fill up much much slower than with sling. Damage is slightly better and is calculated by: 75* sqrt(q of bow / 10) + arrow damage. With bows you need also as good arrows as bow itself if not better. For that you need to get good q branches and stone or bones. Also you need to have quiver equiped this making a slot for backpack used and you need both hands free to equip bow. In one quiever you can carry around 40 arrows. I don not reccomend to use bows until you have merchant robe (makes your inventory bigger while wearing quiver and using bow) and at least 140+MM skill.
Ranger's bow is best ranged weapon in game and you aim 6x slower than with sling and 3x slower than with wodden bow. But their damage is calculated: 300*sqrt(q of bow / 10) + arrows. As you can see ranger's bow has much much more damage as wodden bow and wodden bow has slightly more damage as sling making wodden bow kinda not very usable. Also ranger's bow costs a nice sum of materials and getting good q is a lot of work invested. Having low q of ranger's bow only lower your efficient MM skill and make them useless (would be same as not having enough MM skill and try to use a bow).
When you don't have enough or high MM skill, your aiming bar is filling up very slowly. Sometimes it won't even fill up to full at all. So bar fill at full make u hit with 99-100% and all empty bar with make u hit 0-1%. Now calculate by yourself when you see bar filling up. So when you want to fire with ranged weapon, wait for a bar to show up and fill up a bit, and then fire. At start you will miss a lot, but after some time and LP invested in MM you will aim faster and more accurate.
So my advice: get good sling up to MM 140, after that search for q70+ ranger bow.
Oh and don't forget:
when you fire with wodden bow and it's quality is for example 40 and you have 100MM skill you will aim as having only 80MM. This also affects arrows. If you have 100 MM skill and wish to use wodden bow, make sure it is at least q50 and arrows 2. Quiver q don't affect shotting at all.
When you fire with ranger bow and it's quality is 50 and you have 200MM skill you will aim as having only 150MM but 6x slower as you will fire with sling at 150 MM skill. This is why low q ranger's bow doesn't make any sense to make and use it.
More read at:
http://havenandhearth.wikia.com/wiki/Archery