Well, I can tell you from my own experience, as I play about the same amount as you do. I played a number of years as a junior and learned there, but when I returned to the game a number of years later I had never received any further help from a pro in the form of a lesson. Now keep in mind I was able to build a foundation as a jr. I have shaved a number of strokes off my cap over the last couple of years but I have reached as far as I can go on my own. I hover around a 2 or 3 but there is a big gap to a 0 from there, and that requirs work and practice time.
My advise is get a lesson or two and get a base in fundamentals, once you get a base you can work on that on your own by practicing. If you don't practice or get a lesson chances are slim to make it to scratch.