If you are not familiar with the California "Green" vs "RED" sticker issues then you should read up on that. Here is the DMV webpage:
http://www.ohv.parks.ca.gov/default.asp?page_id=1140
Basically, starting in 2002 California started imposing restrictions on off road vehicles that do not meet the EPA requirements. A green sticker bike is allowed to ride year round, while red sticker bikes are banned during portions of the year, usually most of the summer and sometimes into the fall.
Bikes 2002 and older are grandfathered into a green sticker.
It took the bike manufacturers a couple of years to get their models into compliance, so you will see certain models that were green sticker in 2002, red sticker in 2003 - 2005 and then are green sticker again in 2006 to present.
At many areas the sticker regulations are not enforced and many people get away without having any sticker at all. The Mojave desert is such a place, it simply has too many access points and is too large of an area for the enforemcent to be effective but there is always the chance that you will get stopped and cited.
The OHV parks in the forest areas are often very tightly regulated. At a state park near where I live, Hollister Hills, you enter through the ranger kiosk and the bikes are 100% inspected. You won't ride at Hollister Hills without a sticker appropriate for the season.
That said:
The bike that comes to mind for you is a Yamaha WR450F. I know the 2006 and later models are green sticker, I have heard conflicting reports about the 2005 model, and the 2003 is red sticker.
Rod