Welcome to RTA!
Michael has given you much good advice. My husband and I have tried to do that trip in two days, but we ended up regretting it BIG TIME. That first night, near Red Bluff (we actually made it to Lakehead on the northshore of Shasta Lake), made it a doozy of a day, and the next day was no picnic either. Yet another time we did it in 3 days and it was much, much better. (First night in the Bay Area, 2nd night in the Rogue River area of Oregon, and third night in Olympia, WA.)
I would take Michael's advice and fly, if you're by yourself. Then rent a car when you're in the area.
Donna in San Diego County