1) It is always much less expensive to stay in So. Lake Tahoe, particularly mid-week when you will be in CA. You might find rooms in casinos like Harvey's or Harrahs for less than $60 that are within walking distance to the Heavenly gondola (the prices now for your date is around $100 per night, but that could drop a few weeks before you will be there if the rooms aren't filled). Most of the motels are poor, so look around for reviews for the better ones. Some go for as low as $30 or less per night, but I wouldn't stay in them. It costs a lot more in Sacramento for a hotel, so you might as well go east.
2) There are usually no bus rides mid-week but check with the Bay Area Ski Bus to see.
3) The drive is easy when there is no traffic and the weather is good. Remember, rush hour sucks in the Bay area and around Sacramento.
4) Whether you take 50 to South Lake Tahoe or 80 to the north to Sugar Bowl, Squaw or wherever is up to you. There is plenty of snow and it will last through spring. Heavenly and Homewood have wonderful views of the lake.
5) There is a lot to do in the Bay area when coming back. Consider wine tasting, seeing a show, etc.
6) If you go to the southern part of Lake Tahoe (Heavenly or drive over to Kirkwood) consider visiting the wineries in Amador County on the way back to SF.