Thankfully you will not have to re-register with the state of Virginia and can maintain your Washington motorcycle registration without any problems, as that will remain your permanent place of residence. The requirement that you register your vehicle in the new home state only applies when you establish residence in that state. Since you are not permanently staying in Virginia, and only staying at a month at a time, you are not under any obligation to have your motorcycle re-registered once you get to Virginia. In Virginia, you would be required to re-register your vehicle (and also obtain XXXXX XXXXXcenses) within 30 days of establishing residence.
However, since you're only going to be there temporarily, although for three months, you've yet to establish residency according to Virginia law and are free to ride your motorcycles with Washington plates, registration, and licenses. This is especially true because you seem to imply you're going for enjoyment rather than employment. Anyway, happy trails, I've heard Virginia is for Lovers, so it should be a great place to ride with your wife. (E.g., out-of-state college students don't have to re-register vehicles unless making the new state a permanent residence).
This is from the Virginia DMV page relevant to moving to Virginia:
If you are a non-resident temporarily living in Virginia, you may drive with your home state or country driver's license and license plates for no more than six months. This does not apply to commercial vehicle drivers. If you become gainfully employed, you are required to hold a Virginia driver's license.