Most likely, you will have a round rear, but I'd hate to tell you the wrong thing. Lapping the rings is a process that trues the rings to give a straight grip on your scope to avoid exerting any flex on your tube, or having an edge of a ring bite into it. You install your base and rings. Then you take two pieces of metal rod and mount them in the rings. Both bars will be tapered to a point on one end. These ends need to point toward each other. If your set-up is true, the ends points will line up perfectly, telling you that your scope rings are perfectly aligned. If they are not, they need lapped. To do this, you place a metal bar that is (1" diameter), with a lapping compound applied, in the lower half of the rings. Secure the top half of the rings to the bottom half "mounting" the lapping bar. Slowly polish the inside of the rings with the bar. Do it a little at a time while remounting the two alignment bars and checking their position often. It shouldn't take much lapping to square up the mating surfaces. There are kits availabe for just this process. They will have more detailed directiond. Or you can just use the burris signature rings and forget all about the headache of worrying if your set-up is trued. The inserts will automatically self-align to the scope tube. I know of no easier way to protect a good scope form mis-aligned ring damage.
As for bedding, doing the action is not a bad idea, but I was talking about bedding a scope base. This is just like bedding an action in that is creates a new mating surface to bolt against, and it is one that perfectly matches your base so that when you tighten it down, it isn't flexed. Many actions and one piece bases won't fit flush to each other. To allow them to blot together without stress, you need to fill the void with a bedding agent. If you go with a two-piece base, you don't need to worry about it.