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It appears I am in luck as there are quite a few GF friendly restaurants in the Bethesda area.  Below are the responses I received.  Thank you so much to all with such helpful info.  Also, I received a list from the head of the DC support group but have misplaced it.  If I get another copy of the list I will post it.

Lilit is amazing!  A small cafe but great food - there is a refrigerated section in the back with cookies, cakes, etc, you could purchase to take back to your room - 

Shanghai Garden - ask for Rae, the owner
4469 Connecticut Avenue Northwest Washington, DC 20008-2302 - (202) 362-3000

There is a P.F. Chang's about a 5 minute drive away at the White Flint Mall.

5 Guys always works for us.  Everything they have is gf except the bun.  So, the fries are safe! 

Almost everything on the menu at Don Pollo is GF. The only thing that might have gluten is the corn bread. The one in Bethesda (I believe there are a couple others) is at: 
 7007 Wisconsin Avenue 
Chevy Chase, MD 20815-6106 
(301) 652-0001 
 I get the 1/2 chicken with plantains and yucca, which is what is pictured on that page. You don't need the sauces. As pictured is $8.75 if you get water. 
 
Then Bethesda, like most places, has a variety of Indian restaurants, and like all Indian restaurants all curries are GF. 

The Washington, DC, support group has an extensive restaurant list at:
http://dcceliacs.typepad.com/washington_dc_celiac_supp/favorite-restaurants.html
In Bethesda they list:
Assaggi Mozarella Bar 
Austin Grill
Café Delux 
Cesco Trattoria
Cosi 
China Pavillion
Delhi Dhaba
Fancy Cakes by Leslie
Hyatt Regency 
Jaleo
Grapeseed Bistro 
Lebanese Taverna
Levante’s
Lilit Café
Louisiana Express Co
Louisiana Kitchen and Bayou Bar
McCormick & Schmick's
Mon Ami Gabi
New Orleans Bistro
Organic to Go 
Original Pancake House 
Passage to India 
Raku Asian Dining 
Rio Grande Cafe 
Sweet Basil
Tara Thai
Vision’s
 
I can personally recommend the Austin Grill, Jaleo, the Original Pancake Houe, and Tara Thai. I've been meaning to go to the Lilit Cafe the next time I'm in the area, but I haven't made it there yet. I've only heard good things about it, though.

http://www.examiner.com/x-5121-DC-Gluten-Free-Examiner~y2009m11d11-10-restaurants-in-Bethesda-to-eat-gluten-free
There are many good gf friendly restaurants in Bethesda. So many, I wish I 
lived there. We visited our son on the weekend and we went to my favorite one-Mon Ami Gabi. 
They have a great gf menu which includes onion soup (yum) and bread. Also in 
Bethesda are Maggionis - gf pasta, PF Changs -gf menu.

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