Napa is very beautiful and the wines are top notch but it is also very expensive and can be quite pretentious. Plan on spending as much as $50/day just in tasting fees and many wineries don't credit the fees towards a bottle purchase!
The wineries are not close enough to one another to walk, for the most part. Two north/south corridors dominate the valley; Hwy 29 on the western side, and the Silverado Trail on the eastern side. Most of the towns lie along Hwy 29. The "Trail" has much more production of grapes along it and many of the best wineries. Also with the trail, it's more local traffic while 29 is a stop-and-go tourist parade most weekends. You may literally be able to walk through St. Helena (one of the main towns) faster than you can drive through it most Saturdays.
I would recommend a car tour rather than a bike tour. As others have said, it's very hot during the summer (fall is beautiful) and the heavy traffic takes away from the pleasant experience of a bike. Also, biking leaves you with no place to carry any wine you purchase. Many, many maps are available that give suggested tour routes. Be aware too that since it is snooty Napa, many wineries require a tasting appointment which can be made 24 hours ahead of time usually.
Now that I've said all that, I would actually recommend at trip to Napa's neighbor, Sonoma. Sonoma county makes wines easily as good as Napa's, but still isn't overrun with tourists. Use the small town of Healdsburg as your hub, and spend a day each touring through Dry Creek, Alexander Valley, and the Russian River Valley to the south. All are in a 10 mile radius of Healdsburg and feature unique wines to the region (DCV-Zinfandels, AV-Cabs and Sauv Blanc, RRV-Pinot Noir and Chardonnay)
Lived in Sonoma for 3 years. Work in the wine biz.