In the states, if you rent a car, and you have current insurance that covers "comprehensive and collision" (you are covered for theft, damage from natural disasters, or an at-fault accident) this will normally transfer to the rental car in most cases. If you only have liability (I think its called "3rd party" in the UK), this, too, will transfer, but you are still responsible for the "comp and collision" part, which is conveniently offered through the rental company for a dear, daily premium. (Keep in mind that every US state has its own laws, so this might not apply to every US state!)
I don't know if all of this transfers to the motorcycle rental business. It seems that if you purchased US insurance on a US registered bike, then this will (normally, depending on the state you are in) transfer over to the rental. However, if you had a US registered bike, then you would not be needing a rental, so it seems like you will be stuck with the company's insurance if you went the rental route.
The only way out of this is to actually purchase a bike, which might not be too outrageous given the value of the dollar, and the fact that you can get good deals in cities that are heavily populated, such as the greater metropolitan Los Angeles area--KLR650's a few years old going in the $3K range.
You can sell the bike before you leave, even at a loss, and still be ahead compared to a rental. Just something to consider.