[ReconViper 1]

You should be able to purchase a gun from the Virginia dealer and have them ship it to an FFL in your home state. You can pick it up there and make out an ATF 4473 report for approval of the sale.

[verum ago]

Some other shtuff:

I don't see any restrictions here:
Firearms purchase eligibility test (Virginia State Police)

FAQ Down the page a bit:

What are the laws concerning the private sale of a handgun?
To privately sell a firearm, it is recommended that you safeguard information pertaining to the transaction such as the date the firearm was sold, the complete name and address of the buyer, and the make, model, and serial number of the firearm. The seller and buyer of a handgun must be a resident of the state in which the transfer occurs. Should the firearm ever be located at a crime scene, trace of the firearm will determine the licensed dealer who last sold the firearm and will identify the last buyer of the firearm. To have your name removed from this process, you may consider placing your firearm on consignment with a licensed dealer. This will also ensure that the firearm is transferred only to a lawfully eligible individual.

[PowderMonkey]

Only a Virginia resident may purchase a handgun in Virginia. If you reside in an adjacent state, you may purchase a long gun in Virginia. Otherwise, the transfer must be handled between the dealer in Virginia, a federally licensed firearms dealer in your home state.

[Hot Tabasco]

I was at a gun store in Virginia this past weekend and was told that Virginia law states that only VA residents can purchase a gun in VA. Is this true.

Handgun or rifle?

Handgun sales are subject to state laws and state residents. While hunting in Kansas a number of years ago, we took a day off and drove up to a Cabelas in Nebraska. I saw a nice .22 handgun that I was going to buy but I couldn't unless it was shipped to a FFL dealer here in Michigan and that defeated the purpose.

[BulletBobCo]

It’s been over 20 years, but I believe if you are in the military stationed in VA, you were exempt from this rule.