I shot in the Tri County Gallery (.22 bulls-eye) League for a few years. I started with iron sights but quickly switched to a dot. My scores went up significantly. In fact, If you look at the top shooters, nearly all are shooting dots these days. Why? because in the rapid fire stage, you can be much more precise and speedy in getting back on target.
That said, while you don't need to spend a ton of $, you do need a dot that produces a 2-3 min dot (TOPS) so you can precisely aim for that tiny X. Larger dots will blot out the 10 ring and actually cost you points.
BEst of luck, it's allot of fun!
I shot some bullseye in the past and intend to again in the future. I have an astigmatism as well (and while I don't associate that with the reason behind not liking a dot), I found that I preferred reticles with an outer circle- which made seemed to make centering easier.