What a great adventure you have planned!
First, there will be two distinct tasks when you buy your motorcycle here in California: transferring ownership (title) and getting it licensed (registration). Actually, there is a third: paying taxes and fees, but you cannot do the first two without it anyway so I don't count it separately.
I've been a California resident for over half a century and have bought/sold many, many vehicles here. I've found that it's never the same twice! It sorta depends on who you get when you finally step up to the counter at the Department of Motor Vehicles (DMV). But here's the basic procedure:
First you transfer the title. The seller will provide a "pink slip" (which has not actually been pink for many years but it will be called a pink slip until the end of time). He/she signs it to release ownership interest. You fill out your part of it, present it to the DMV clerk with a bill of sale (more on that in a second), pay the "use fee" (sales tax by another name), transfer fee, etc., and the vehicle is legally yours. No driver's license should be needed because anyone, even a child, is legally allowed to own a car if they want. They just can't drive it.

But it never hurts to have a license because that's the de facto universal identification document here.
Back to that bill of sale: Legally, a handwritten note on the back of a bar napkin will suffice. However, if you want to get in and out of the DMV office with the least hassle, download the official DMV bill of sale form from their web site
http://www.dmv.ca.gov/forms/reg/reg135.pdf and have it filled out before you step foot into the DMV.
Important note: Almost everyone tries to cheat by putting down a price lower than they really paid. It's up to you, but be aware that the DMV is not stupid and they have computers. Also, taxes are the way we pay for our roads. Also, being honest is simply a good way to live. I'm just sayin'.
The second major step is vehicle registration. I'm not actually sure how they'll deal with registering a vehicle to someone who is not a resident of California, but my guess is they'll do it happily -- because, of course, they get to charge more fees! There's a registration fee, a license fee, a transfer fee, a moon-phase fee, a fee payment fee, and probably a fee determination fee. Just kidding on the last ones, but it sure seems like that when you see the form with about four columns of mysterious fees.
When you've successfully registered the vehicle they will usually issue your license plates on the spot. (Actually it's license PLATE, singular, for motorcycles.) But they will need to mail you the new title because that must come from Sacramento. They will give you a temporary title document so you have something to prove the vehicle is yours, but you will need an address so they can mail the real one to you. If you won't have an address here, get in touch with me.
The DMV main site is:
California Department of Motor Vehicles
Info on buying/selling a vehicle:
Buying or Selling a Vehicle (Changing Vehicle Ownership)
Info on title and registration:
Vehicle Registration and Title Information
Info for exporting a vehicle out of California:
Vehicles For Exportation
And if you plan to ride in Northern California when you're here, let me know! I'll buy ya a cup of coffee at my neighborhood coffee shop, and maybe ride with you up to the world-famous Alice's Restaurant on Skyline if my schedule allows. Usually not difficult to talk me into THAT.