About ⅔ or two thirds of the way, you can stop at Potomac, MD. This is about half an hour east of Dulles, or about 10 minutes southwest of Rockville.
About ¾ or three fourths of the way, you can stop at North Bethesda, MD. This is about half an hour east of Dulles, or about 7 minutes southeast of Rockville.
If you drive straight through without stopping at all, the total distance is 27 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 32 minutes.