riverain, I live right near you and you’re right, Rockville Pike is a tricky place to bike. I second the recommendation above of the Bethesda Trolley Trail. For the stretch of the Pike between the intersection of 355 & Veirs Mill and Twinbrook Metro, I find that Lewis Ave., immediately to the east of the train tracks, is a good bypass. From Twinbrook you can take Chapman Ave. and thread your way through parking lots to get to Montrose, crossing on Maple Ave. out of the Montrose Crossing center.
For times when I’m forced onto the Pike I find that the parking lots are much more comfortable to bike through than the sidewalk (I don’t even consider using the traffic lanes, way too scary). On the west side of the Pike, there’s always East Jefferson–>Executive Blvd to get you to the trail.
Good luck! I’ve noticed that the number of cyclists along and around the Pike is growing. Hope you’ll join us.