Hi Rick
My recent computer racing hobby started with a motorbike sim, it's still some of the most fun racing on PC I find (much more overtaking, much more crashing...)
Ain't much available on PC currently, sadly. The MotoGP license is with Capcom which are only doing it for PS3 and Xbox. The last MotoGP title for the PC is MotoGP08 programmed by Milestone.
Personally I really like SBK-X, last years Superbike World Championship game with the official license (also done by Milestone). SBK-2011 is out now (at least in EU, not sure about US), but I haven't played it, and as far as I can tell it does not offer a lot over SBK-X other than the current season.
SBK-X is nice in that you have three classes - Superstock 1000, Supersport and Suberbike - where you can run single race, race weekend, championship in either of them, but you also get a very good career mode that has you signing contracts with smaller Superstock 1000 teams and working up to eventually land a Suberbike season contract.
Only downside of the SBK-X game and also SBK-2011 is that it only runs in 16:9 aspect ratio. You get black bars on any other screen ratio, especially bad on 4:3 and 5:4 obviously. If you have older hardware and are running an older screen, you should look at MotoGP08 which does multiple aspect ratios.
Ideally you'll want to get a gamepad for those titles. SBK has you controlling two brakes separatly, and also leaning the rider forward/backward. Coupled with manual shifting, that's a lot more buttons than you can fit on a joystick. But you can auomate rider balance and shifting, obviously.
There's also GPBikes, a Pre-Beta Software that currently has no AI, no official licensed bikes, not much else, but it is a very good simulation. Just not developed into anything yet.