You can sum up Claremont's transportation system in five words: not really all that good. Some students seem able to navigate the confusing waters of public transit, but many more get hopelessly lost, and some are probably still riding the bus today, haggard and tired, traveling from poorly marked bus stop to poorly marked bus stop, somehow getting ever farther from home. The buses are really slow and nightmarishly confusing, but the train, which is right next to campus, is very fast and easy. Unfortunately, the last train back from LA is at 8 or 9 p.m., so unless you plan on spending the night, evenings in the city require a car.
This really is one of the most frustrating things about going to Pomona: feeling so confined and being so close to Los Angeles yet being unable to get there. It's doable, just very frustrating and difficult, and it's generally not worth it. Cabs and the super shuttle work great for getting to the airport, but they are expensive for travel to LA. The only real answer is having your own car.