Few hills or many?
Getting up to the Custis Trail would be the "scenic" route, and add a few miles. Probably good for training but maybe not for getting to work in a timely manner.
This way is more direct, but a bit twisty.
From around Rolling and Braddock, cross over to King's Park and pick up the end of the Accotink Trail (near the VRE tracks) and go around the lake, past the marina. Continue around and there is a side trail on the right that takes you into the neighborhood and up to Queensbury (you'll go right/east on Qby)
(or if you don't want to deal with a gravel take Clydesdale to Danbury Forest to Braddock (traffic) to Queensbury)
From Queensbury, left at T at Hemming. Go under the B'way and first R on Leesville.
Left at T onto Backlick (traffic) and right at light on Edsall (busy but wide). (You could use Industrial Road to avoid the traffic, but there are a lot of trucks and the paving is bad.)
Just before Edsall reaches I-395, go left on Cherokee Ave. When you get to Chowan bear right and continue to Little River Turnpike.
I don't think there is good connection east that avoids traffic, so take just LRT to Beauregard. added - might be a service road in front of the apartments.
From here the simplest would be Beauregard to Walter Reed to Arlington Mill and down to Shirlington. Take the pedestrian bridge over I-395 and down the hill on Martha Custis.
(If Beauregard seems too busy for you, take it as far as Sanger and cross under I-395. Stay straight onto Richenbacher, left on Pegarm, right on Seminary, left on Howard, right on Braddock, left on North Early, right on Menokin. Take the King St service road to Wakefield. Cross at light on Wakefield. Right at S. 34th St, left at Stafford, right on Preston. Cross Quaker lane and Preston joins Valley which joins Martha Custis near Glebe. A lot of zigzags, but it's pretty and not too busy)
Left on West Glebe and on the other side of the bridge take the side path along South Glebe (Four Mile Run Trail).
Then you could take the 4MR to the end of Eads Street (good the bike lanes). Then 18th Street and Hayes to the Pentagon Mall. In the parking lot across the mall there is a pedestrian tunnel under the highway that takes you into the Pentagon south parking lot.
Or if you want something more scenic, stay on 4MR to the Mount Vernon Trail and up to the Memorial Bridge connection. Between Parkway crossings take the trail on the left which leads (eventually) to the Pentagon north parking lot.
I know it's a lot of turns, but it's not too bad a ride. I've biked about 90% of it (just not in rush hour) and driven most of the rest. (Local knowledge is better than any map.
There are also lots of variations to make it interesting, like cutting over from Beauregard to Chambliss and Dawes, or going thru Annandale and around Lake Barcroft on Waterway and Beachway to get to Dawes from the north (this is a hilly one.)
Let us know route you decide on.