It looks like you could do the whole ride on bike trails. Drop into Rock Creek on Shoreham Dr. (Calvert and 24th). Connect to C&O tow path for the scenic route through Georgetown to Key Bridge. In Virginia, take Custis Trail to George Mason Drive. According to my map, there's a bike path parallel to George Mason Drive that will take you within blocks of your destination. I never rode it, if it turns out to be a glorified sidewalk, you might try getting off Custis Trail at Quincy and working your way due south through the neighborhood. Looks like you can find a nice route, short, easy ride! Have fun!

You can take the long way if you have time and want more miles. Custis Trail or Mount Vernon Trail to Four Mile Run, Route 50 access road from 4 mile to office. If you are running late, shoot down Conn to Florida to M st. I always use the side walk (left side both directions) on Key Bridge and I don't feel like Wilson saves much time over Custis Trail but you can ride Wilson for variety or maybe faster.

ccrider is great at figuring out good routes for commuters through the DC area. Hopefully he will answer this thread.