I suggest you NS to IAD. Weather can be problematic if you Xfer in ORD or DEN at this time of year. I avoid these Xfers in winter if at all possible.

Once at IAD, since you're not in a hurry:

(A) either do the 5A bus http://www.wmata.com/timetables/dc/5a.pdf - the buses do depart on time and arrive pretty much on time, the cost is $3. One of the last remaining bargains in DC. The bus lets you off at the Rosslyn Metro stop. From there grab either 1) the Orange or Blue line (they run on the same track for the trip you will take) to Metro Center and transfer to the Red line to Bethesda or 2) take the Blue line to King St. Be sure to check you're heading in the right direction since the Blue line you will take in both options will be heading in different directions.

or (B) take the Washington Flyer bus http://www.washfly.com/metro.htm from IAD (this bus leaves from the upper level not the street level, you'll need a ticket from the ticket booth near the outside door (I think it's door 4, but not sure, click on "Location Map" here: http://www.washfly.com/). This will deposit you at West Falls Church (here's a system map: http://www.wmata.com/metrorail/systemmap.cfm. This will cost $8 plus the metro fare from West Falls Church. If you're going to Bethesda stay on the Orange line (that's the only line at WFC) to Metro Center and change to the Red line to Bethesda. If you're going to King St. change at Rosslyn for the Blue line to King St. as with the 5A bus.

Bethesda and King St both have the advantage of many good restaurants in the neighborhoods. As to the zoo, I usually recommend arriving via the Cleveland Park station then walking downhill to the zoo and then continuing the walk downhill to the Woodley Park station. If you want to eat near the zoo, most of the better restaurants are around the Cleveland Park station, but there are a few good ones near the Woodley Park station as well. Depends on your tastes and pocketbook.

Bon voyage and happy pandaing. Say nin how to the mini-panda for me.