Speaking as someone who has a fair background in paleontology, I think you're looking at it the wrong way. Being bipedal may not have been much of an advantage at all.
Theropod dinosaurs literally couldn't become quadrupedal if they wanted to. The wrists of dinosaurs are often shown improperly in illustrations, but it would have been impossible for them to rotate their hands for their palms to face the ground. Birds inherited the same wrists, although since they have wings, it's become even more unlikely they'd make a reversal.
Being bipedal sucks in a lot of circumstances. It's very easy to lose balance for example, so prey could just knock one leg from under a predator and make them fall. Also, climbing in mountainous terrain is much easier on all fours, as anyone who's done some hiking can tell you.
Some things about being a biped are useful. For example, you can be a really fast runner. But it seems this isn't the case for mammals, because we have a flexible spine, like reptiles, and lack the rigid backbone which dinosaurs have and birds retain.
And as an aside, humans became bipedal more or less because we didn't have a choice. It's now thought the ancestors of humans, gorillas, and chimps were all somewhat bipedal when they were on the ground (like modern day orangs and gibbons are). Ape wrists are different from monkey wrists - if we ran on our palms, we'd shoot our wrist bones out in short measure. Gorillas and chimps evolved to scale tree trunks, became bow-legged, and had to resort to knuckle-walking, but we kept the ancestral bipedal gait.
