In Mario Kart DS, you could go into Versus in single-player. You'd pick your character, your kart, your course, and off you go, playing that one course against a full field of CPUs, with items and everything. If you were addicted to, say, Waluigi Pinball, you could endlessly play that course, firing shells, dropping banana peels, etc.
According to the U.S. website for Mario Kart 7, however, you can't do that in the new game. Versus is for multiplayer only. If you want to play against CPU with items, you'll have to do so in sets of four tracks at a time. So if you want to play against CPUs on Rainbow Road, you'll have to play through the three courses before it first.
Terrible, terrible news. I thought single-player Versus would be a lock, given this is a pick-up-and-play portable, and given the fact DS and Wii had it. Instead they've gone back to the Dark Ages. Goddamn it.