I don't know if you can purchase car or motorcycle insurance in the U.S. unless you have a valid driver's license here (I very much doubt it), but there should be some options open to you.

You should be able to get travel insurance in the UK that will cover you for the liability of driving in the U.S., though I'm not sure if such policies cover only cars. I'd look in that direction. It sounds convoluted, but you have many travel insurance options in the UK (more than we have in the US), so I think you can find an option.

We have several UK-based posters here, so perhaps you'll find a clearer answer from one of them, though I don't know if any are motorcycle riders.

Another viable option would be to become a licensed driver in the state of California. That might be possible.

I think that you would have trouble registering a vehicle in the US without a local address and a local license. Also, proof of insurance - meeting the standards of the particular state would be required.

I don't know what they are in CA (in some states I believe required liability is as low as $10,000) - but in a state with a lot of expensive vehicles I would want much more than that - unless you are judgement proof (have no assets). (Our liability in NYC is $300K/$500K - again since there are a lot of expensive vehicles out there - and $10K barely covers an old clunker. And you can get better rates if you go for a higher deductible. Ours is $1000 versus the standard $500. If you want coverage with no deductible, costs are usually outrageous. Also - you need to determine if you want collision coverage - for your own vehicle.)

You do not need to have a CA driver's license in order to buy a vehicle in CA. You must have insurance verification in order to finance a vehicle, but not if you pay cash.

The tricky part is the registration~in order to register a vehicle with the CA DMV, you must show proof of insurance.....do you plan on registering the vehicle in YOUR name or your girlfriend's?

The best way is for your girlfriend to buy/insure/register the vehicle. (If it is a motorcycle - does she have a motorcycle license?)

If it is a car - no issues. You can pay her back but the car will be registered in her name and you can drive it while visiting.