I took me about 5 years to get my first buck with a bow. I started archery hunting at 13, and shot mine shortly before my 18th birthday. I had a TON of encounters with decent bucks in bow range throughout those years, but I didn't know a dang thing about what I was doing. I'm now 23 and haven't shot another buck with a bow yet. It can be frustrating, because in the last two years I've learned a ton, and finally consider myself a serious bowhunter. I put the scout time in, I'm careful with scent, I hunt the wind, plan exit/entry routes, I'm better at reading terrain, etc, but I still haven't been able to connect since that last buck. I've taken does with my bow, but no bucks since that first and last in 2002. Hopefully I've actually learned something, and I'm not just repeating my ignorant ways.
Anyways, I wouldn't get too bent out of shape about how many years you go, because frankly it's hunting. Shoot what makes you happy, and if a shot presents itself that you want, take it. If not, it will eventually.