These months, I would recommend you carry tire chains and have practiced on how to install them (properly). It is easier to practice down here, than up there with freezing fingers. I have had to help too many people @ Big Bear, putting on their tire chains. The police can stop you on the mountain and check if you have tire chains in the car(if you are prepared). If you don’t, they can have you turn around. Most newer cars use ‘cables’ instead of ‘chains’ on their tires.

It does take more than two hours. Up to the foot of the mountain takes about 1hour 45 minutes, pushing it. Another 45 minutes plus to get up the mountain. As mentioned by SD Realtor, there are two ways from the south side of the mountain. Highway 330(Running Springs) and Hwy 38(Redlands). (You may need to zoom out after clicking on the link.. When I tested it, it came in right and then automatically zoomed in.. )
http://maps.yahoo.com/#lat=34.187949854182705&lon=-116.81694030761719&zoom=11
Highway 330 is more consistently plowed, but it has a serious weakness just outside of Big Bear. It runs exposed on the south side of a major slope. This is the area that several people got trapped driving home during a snowstorm. Highway 330 is still undergoing repairs from a slide.. so there are areas where there is one-way traffic. Right now, Highway 38 requires chains. This is a good website for current road conditions, the individual highways have links to their CalTrans status(s): http://www.snowsummit.com/ski/snow-report/current-snow-report/#roads

The back way that SD Realtor mentioned, is highway 18 (Lucerne Valley). You will need to take Highway 15 into Victorville to get Highway 18. Mountain traffic tends to affect Highway 330 most, though I have been caught in traffic on 18 when someone decided to drive like an idiot.

Have fun and drive safely.

NOTE: I may have the zoom-in defeated on the map link above. It looks like Yahoo’s interface becomes brain dead when you have the location specified within the URL’s ‘q’ parameter.