This is, I believe, a Northern black widow (Lactrodectus variolus). I say "I believe" because 1) I'm not a specialist of spider taxonomy and 2) I'm identifying this spider from my photos and not the actual specimen. Mature female Southern black widows, Lactrodectus mactans (the spider we think of as the "classic" black widow), are usually a shiny jet black with just the infamous red hourglass mark on their abdomens, but males and immature female L. mactans do have markings similar to these pictured here.
So why do I think this is L. variolus and not an immature or male L. mactans? The body of this spider was about a half inch in size, suggesting that it was a mature Lactrodectus female. Mature males are only about half that size. Again, the white bands on the dorsal side suggest L. variolus, but there's a better way to distinguish between the two species.
The red hourglass marking on the ventral side of the abdomen is incomplete in the Northern black widow. In contrast, the hourglass is complete with both triangles touching in the Southern black widow. My spider doesn't have a complete hourglass with both triangles touching, so I think this a Northern black widow, L. variolus.
Initially it may sound funny that the Northern black widow can be found in southwestern Virginia, but there's a good deal of overlap between the ranges of the Northern and Southern black widows. In fact, the Northern black widow can be found as far south as Florida and as far west as Texas, while the Southern black widow can be found as far north as parts of Canada. We have both species on our property, with a healthy population of Southern black widows in the stone block wall edging our driveway.
For more information about Lactrodectus spiders, Bugguide has great information on the genus Lactrodectus on their website and you can also find some terrific pictures there, too. And if you have any burning questions regarding these spiders or if you think you have one in your house, please contact your local extension agent for more information. Don't think you have a local extension agent? Don't be silly, they're in all 50 states of the USA and you can find yours here at the USDA website.