In which state is the bike registered?

Only I looked at this as I was going to buy a bike and leave it there, it wasn't the registration that stopped me but insurance. I have family in NY state but you must have a NY state license, friends in NH, you must be a NH resident. Last time I insured the bike in Maryland as that looked foreigner friendly.

We put our bikes in a storage locker in Las Vegas. Nice dry climate. The facility is behind the Holiday Inn, 1 mile from the BMW dealer and they have a free courtesy bus to the airport.

Do keep in mind that neither insurance nor registration fees need be paid whilst said machine is OFF public roads and in storage on private property.

In California we have something called "NON Operational status" cost $10.
Once bike is returned to road, no penalties are assessed and fee is prorated based on time of expiration of past registration. Be sure to get this status if storing in a state they offer it. (will save some money over long term storage .. . like over a year)

Insurance companies like to have you "continue" your insurance, even when stored, but it is not legally required in ANY state. But .. generally speaking, a year long policy is cheaper than a short term one. Some states have Summer only policies. (not California) But if you're gone for a year or more ... then CANCEL your insurance ... and tell them why.
Should be no problem re-instating policy once you return to USA.

So, ask about non operational status for the state you are registered in. Or ... if storing bike FAR from it's "home" state ... transfer it to state in which it is stored once you return to USA and wish to put it back on the road. All doable. You will need a local address for them to send you your title/registration.

DMV's don't (can't) ask for proof of insurance at time of registering .... in California you have 10 days to obtain insurance. Insurance company will electronically notify DMV once you buy insurance.

When you re-new your insurance policy each year (or when ever), the company emails DMV stating your insurance is valid. If NO insurance is shown, (in California) they will revoke your registration. (Not Good)

Keep reaching out to HUBB communities for storage options. I have NO ROOM ... so no chance I can offer a spot for your bike. Sorry!