Why not Montessori?
There is small, low-key Montessori school that's been in downtown Bethesda for 30 years called The Bethesda Montessori School - cheaper than the newer ones but very good care (and excellent academics, obviously). My children have been very happy there.

http://www.bethesdamontessori.com/

If you're Jewish, B'nai Israel has a transitions class

Thanks for all the suggestions!

Christ Episcopal School in Rockville is full day preK. Very advanced.

Westmoreland Children's Center, but its basically on the DC border. Might be too close in.

St. James Children's School fits the bill -- on Seven Locks Rd, technically Potomac, but very close to the Rockville border.

JCC Rockville has a TK/K Open House on Dec 10. There is before and after care available as well. From their website....

For children who have completed a program for 4-year-olds, and would benefit from an additional year before entering Kindergarten. Our Transitional Kindergarten program prepares children for elementary school in a small, nurturing environment with skillful, careful teachers. Our TK program creates a dynamic classroom experience that respects children’s ideas and helps them grow socially and intellectually. Literacy, math, social studies, and science are integrated through throughout the day, and learning opportunities happen everywhere, from the classroom to the playground.

Classes meet daily from 9:15 a.m. to 2:45 p.m.

I'm specifically looking for full-day preschools (9-5) that are not Montessori in Bethesda, Rockville or even Gaithersburg (close to Rockville) would work. DD misses the cutoff for kindergarten, so ideally I'd like to also have a 4+ or transitions class. We have been on the waiting list for Rock Spring since she was 6 months (she's 3 now), but it's more than we can pay ($1,600+ a month). I guess coop would be OK, but it would have to be limited coop. We both work FT. It's more difficult to find than I thought. Suggestions?