Increasing your archery skill in Skyrim is based on the amount of damage that you deal rather than the amount of hits you get. With this in mind, you can increase your archery skill incredibly fast simply by finding an enemy that does not have a ranged attack and attacking them from a high location where they can’t reach you. If you have a high powered bow and a lot of good arrows, you can go to the mammoth fields and climb up somewhere high, like a cliff ledge or something. Increase the games difficulty and deal as much damage as you can to the nearby mammoths. They are unable to attack from a ranged distance and they wont be able to reach you if you are up high. You can deal a huge amount of damage with your bow in a short amount of time using this method.
A more useful and less grindy tip is to take advantage of the damage bonus that you get while sneaking. If you sneak and attack an enemy who is not aware you are there, will deal triple damage. In the drauger caves, you will find a lot of them sleeping, you can almost always tell which ones are alive and which ones are not going to move. Attack these enemies while sneaking with your bow to deal a lot of damage and quickly kill the entire cave of enemies. Since they are sleeping, killing one sleeping drauger with a sneak attack using your bow, will not wake up other nearby enemies. Do this as often as you can to quickly increase your archery and sneak skill while making the encounters with the drauger a lot easier and reduces the risk of them ever swarming you.