I don't know how you would quantify the bandwidth without knowing dimensions of the bridge, but let's make some basic assumptions from the facts that we know. The Bifrost is a bridge made of light. We have some basis for analyzing bandwidth of light-based communications using fiber optics. Take a look at the wikipedia article mentioning 100 petabit per second speeds on a single fiber optic cable.
Presumably, since the Asgardians have far more advanced technology than humans, 100 petabits represents a starting point that they long ago surpassed, but let's use it as a starting point. How many fiber optic cables could you lay next to each other across the width of the Bifrost? Multiply that number times 100 petabits and then assume that your final number is, again, just a starting point.
That is the kind of bandwidth that would be needed for a task like tansporting a person from point to point. Consider the number of cells in your body, and the number of cells of the organisms that live on/in your body, and you'll see that 100 petabits isn't as much as it sounds like.
As for scale, if we base our calculations on what we know from the movies, I would say the Bifrost is limited in scale by the design of the system and the amount of energy needed to power it. A circle, maybe ~20 meters (or less) across, is the "imprint" it leaves on Earth. Could it be made bigger? Maybe, but based on the size of the portal on Asgard, you could not send a building from Earth to Asgard. It's seems physically designed for use by individuals and small groups.
Can the chamber be increased in size? Who knows. Again, it seems intended by design to move small groups of people across vast distances so the Asgardians can visit other worlds.