I know of no route on or near Highway 50. What's more, they used to allow bicycles on Highway 50 but most of it is freeway or near freeway now. You could probably ride from Hangtown but you wouldn't enjoy it especially on those damned cliff overhangs where the cars have inches to spare and are traveling at 80 mph.
OR:
There's the bike path that parallels 80 over the hill. At the far end of that road you have to slip your bike under the fence and usually you'd have to take all your stuff off to do that and then repack on the other side. I'm not sure why they didn't put a bike gate in there.
Then work your way across the flats to Davis where you can take your first break.
Ride from Davis to Ione via 104.
Ione to Sutter Creek and the backroad (Ridge Rd?) to Volcano. Then up Rams Horn Grade and onto Highway 88. There's places to camp off of the road up near 89 or you can go over Luther Pass to Pioneer or even South Lake Tahoe if you like. From Ione to South Lake Tahoe is about 105 miles via bicycle route. Most of 88 is OK and quiet but there are a few sucky places.
The route around Lake Tahoe is 72 miles so while you're there leave EARLY in the morning and do a clockwise loop. Coming down from Spooner Grade on Highway 50 there is a parking lot to the right. Inside on the rail there is a button that you push which flashes some lights and tells cars that there's a bike in the tunnel. If you're clear behind you might just as well go for it since the tunnel is only 100 feet long or so and you'd be doing 30 mph. You have to be VERY careful of the killer snow drains on the shoulder and out 3 feet into the "slow" lane where traffic often exceeds the speed of light.
The routes up along Highway 80 are difficult at best. You CAN come back over Highway 80 but you have to take all of the backroads and get on at Donner Lake Rd and off again at exit 161? Lots of pain in the butt riding to get back into Auburn and then it's OK though trafficy to Sacramento.