From what I understand, the Bradford reagent contains Coomassie Brilliant Blue in an acidic solution so both of the (sulfonic acid groups? I'm not sure if this is the correct name- I can't seem to find an answer) are protonated. In this form the dye colour is red. The theory is that in the presence of basic R-groups like in arginine residues, the acidic groups react with the basic groups. I don't understand why this is so? Why do the acidic groups react with the basic groups as opposed to just binding with the free $\ce{H+}$ ions in the solution. I suppose this is a fundamental question about acid base reactions.
Also, why does the colour change when the $\ce{SO3-}$ group is bound to a basic R group residue as opposed to a H+ ion? It is still essentially bound to a positive charge? With the basic residue now being protonated e.g. -$\ce{NH3+}$