I've got a Winchester 54 .30-06 and the scope I put on it is a Bushnell Trophy 3-9x40. Not exactly in the class you were talking about. Although I do need glasses for close work, I'm fine with the reticle and naked eye. It's that bright big circle that I can't get immediately.
The problem you are having is because the scope is not at the right distance. Loosen the rings and move it a little forward, take a look, and if you have to, try moving it a little back. After you think you've got it just right, hold it down and quickly shoulder it as though you saw a 12 pointer running. When the scope looks right every time you do that, tighten the rings.
Sometimes it takes a little fiddling with it to get it right.