Indoor bullseye is shot at 50' on the NRA B-2 (slow fire) and B-3 (timed, rapid fire) targets. In each case, the black is just about 3" in diameter (I seem to recall 3.09") and the paper is about 12" high and 10.5 inches across. The black on the slow fire target includes the 7 through 10 rings, on the B-3 it's just the 9 and 10 rings.
You'll have some shots off the paper at first, especially in the sustained fire stages, and maybe even in slow fire - everyone does at first. Unless you're shooting in a very, very crowded range you've got to really pull one to put it on somebody else's target accidentally. However, one of the guys from my team once shot an entire stage of 10 shots on my target, thinking it was his - that's a different problem. Hitting the target hanger, however, is all too easy for beginners and it really is distracting.
Like Bob, I too stopped scoping my shots during a match. It only led to two things: If I started off well on a stage, I got excited and did worse, and if I started off poorly I got pissed off and did worse.