Good morning Linda,
It will be hard to find much in the way of budget priced B&Bs in Napa Valley. We live in SoCal and have made many road trips to the Napa area wine country. Sonoma county, right next to Napa county has fantastic wineries and is less pricy and less snooty than Napa. You might try checking Booking.com to find lodging in Napa/Sonoma/Mendocino countries. They are all great wine counties, and it is easy to drive among them for wine-tasting. (One place we enjoyed staying was in Glen Ellen, near the Jack London State Historic Park and the Sonoma Botanical Garden. We stayed at the Jack London Lodge there.)
As for wineries, we always stop at Cline Cellars in Sonoma county. Nice wines, reasonable tasting price, and lovely setting. A good place to bring a simple picnic lunch. They have a collection of models of all 21 California missions, which is excellent! I have been to each mission in California and the models are really worth seeing. Also in Sonoma county is the Korbel Champagne Cellars in Guerneville. There is a free tour and a free tasting of 5 wines/champagnes. The setting is very nice, the drive is beautiful to get there. (You may need to make a reservation.)
To be honest, there are so many wineries in the area you will have no trouble going to tastings. We never do more than three throughout the day, and take turns tasting because we don't want to drive impaired. There is the Napa Wine train also, but I feel it is overpriced. Many people love it though, and (I believe) have a meal on board. You can find places for olive oil tastings too.
There is a beautiful drive to the ocean on highway 128, through redwood groves and past wineries as well, just in case you have time to see the absolutely beautiful Mendocino county coast. There are lots of neat B&Bs in the town of Mendocino, and the drive up and down the coast is very scenic. I don't know how much time you have, but the area is so nice to visit that we go almost every year and can easily spend a week or more in this compact tri-county area. There are hundreds of wineries in the area.
You could go in April or May, but May will be somewhat warmer. Almost any month will be nice, but to me summer is too hot.
Have a wonderful trip!