Depends on what freeway you are taking. If you are going straight to Beverly Hills, you wouldn't be getting on the 101 at all. But you would have to be on the 5 freeway at some point, for at least part of the way back, and there always seems to be traffic on that freeway, unless you are driving at something like 6:00 a.m. on a weekend. For example, I live in the Beverly Hills Adjacent area (meaning if you go out of my house and walk two blocks west, you are in the official city of Beverly Hills). It takes 40 or 45 minutes to get to Anaheim on a day with NO traffic (and we would take the 10 East freeway to the 5 South freeway to get down there). On a day with traffic, it can be at least twice that loing to get down there, so weekdays are especially bad.
As far as driving/returning to Bev. Hills from DLR, there have been times when we have been heading back to my house after a day or weekend at DLR, on a Saturday or a Sunday, and we took the 5 North to the 10 West (which is pretty much what you would need to take to get to Beverly Hills from Anaheim), and the freeway was jam-packed in the middle of the day. The 5 seems to have a lot of back-ups due to accidents or whatever reason (last time at DLR, I came back to Beverly Hills from DLR on a Saturday night, and the 5 was closed, forcing us to take side streets for a lot of the way. It took soooo long to get home!). So if you are traveling either North or South on the 5 freeway on a Saturday, I would suggest you do it really early in the morning.
Also a side note, even though everything in this area - my area of town - is pretty close together and easy to access via the main streets such as Fairfax, La Brea, La Cienega, etc., those streets also get very busy. So getting from Beverly Hills to Hollywood or vice versa is simple with a quick jaunt north or south on one of those streets, but there's a lot of street traffic around here so everything takes longer. Everything is in like a 5-mile radius so it is a really popular area - Beverly Hills/Rodeo Drive, Hollywood Blvd, Sunset Blvd., Melrose and Santa Monica Blvd., The Grove/Farmers Market, LACMA/La Brea Tar Pits, the Screen Actors Guild, CBS, etc., etc., and just an extra couple of miles beyond that down Wilshire Blvd. is the Santa Monica Pier and the beach.