I considered doing this once, when I had to fly down to LA for the day and only had a few hours to spare. I ended up taking a tour of the Frank Gehry-designed Walt Disney Concert Hall instead, but I did learn that a visit to the Getty is doable on public transit. I later visited the Getty by car. The art, the building, the gardens, the views are fantastic.

http://www.getty.edu/visit/hours/public_transport.html
http://www.metro.net/riding_metro/bus_overview/images/761.pdf

The Getty Museum is a fabulous facility and collection. All will enjoy. A full day will be stretching the attention span of your teenagers. The food facilities are excellent. You can use the great lunch with a world class view to stretch their patience.

As you only pay to park at the museum, your day might be free.

I am not an expert on LA public trans. My hunch is that a cab is going to be your only option. However, Beverly Hills to Getty is not an extreme distance and might be reasonable.
Calling a cab for your return could be your challenge. Hard to predict how far the cab will dispatch increasing the cost of the return.

Here's our day at the Getty with photos.

http://www.travelswithmaitaitom.com/Tom_%26_Tracy_Home/California_Dreaming_1/Entries/2011/8/14_J._Paul_Getty_Museum_-_Los_Angeles.html

Public Transport is very viable. The Getty Center web site points out that they are a stop on Metro Rapid Line 761 (a bus line). They then direct you to www.metro.net for directions of how to get there from wherever you are. This where your pre-teen and teen can be useful, assuming that they are good on the computer. Assign them the task (should they accept it) of planning your trip. Over on the right hand side of the page there is a section called "Metro Trip Planner". Have them use that to come up with the bus lines and schedules to the Getty from your location in Beverly Hills. And of course for the return. I'm pretty sure there will be a transfer somewhere.

As pointed out, the Getty only charges for parking, so your visit is FREE!

PS. Your post should be tagged California. I have a hunch it was missed by a number of people who might have had brilliant things to say.

As another poster pointed out, the food faciltiies are excellent. It's been about 11 years since we visited, but we had a breath-taking view for lunch at a very nice restaurant. Can't remember if there were more alternatives, but if you can, highly recommend the white table cloth lunch.

Another second on thinking your teenagers might be bored for a whole day. Our solution was to send the kids (with Dad) to DisneyLand for the day and my mom & I had all the time we wanted. Your kids sound a little young to leave alone all day at the pool or whatever, but think about sending them elsewhere so you can really enjoy yourselves.

I think kids 12 and 14 would enjoy the Getty. I was there a few weeks ago and there are so many exhibits and just wandering on the grounds is interesting. I wouldn't sell the kids short by not taking them to this wonderful museum.

Also if you have time is the Getty Mansion in Malibu, not sure about public trans to get there but it is very enjoyable too.

It's about a 10 minute ride on an express bus to Westwood/UCLA, and then about 12 minutes on the 761 bus up to the Getty entrance. $1.50 each way. The restaurant at The Getty is a great spot for lunch, but they are only open for dinner on Saturdays. The garden cafe has good food, too, so make a full afternoon of your visit. 10:00am would be a great time to leave your hotel, after traffic, then return maybe by 3pm to avoid overcrowded busses.

Oops, that's $1.50 per bus. So $6 round trip per person via Metro Bus.

Assuming you mean the Getty Center, not the Getty Villa?

Which is which?

The Getty Villa is on PCH in Malibu and the Getty Center is off the 405.

Getty Villa is a replica of an Italian estate, with beautiful architecture and gardens. It's collection includes amazing antiquities, like jewelry, paintings, glass art etc. Beautiful canyon and other views. Makes a nice stop when driving to Malibu for an outing.

The Getty Center is contemporary architecture, also gorgeous, on a beautiful setting with views of the city. Its collection and style is more modern art.

Both are worth a visit. Both have nice cafes. I've been twice to each of them, because DS and I enjoy them a lot. Admission is free. Check on-line for timed reservation (I think just required for the Villa), and parking policies.