We employed a combination of single chain in mean field methodology and constant pH Monte Carlo framework to compare the influence of charge regulation and charge heterogeneity on the adsorption and bridging characteristics of polyelectrolytes in solution on proteins. By adopting a coarse-grained representation of the proteins as spherical particles and embedding a simple framework for probing charge heterogeneities, we probe the influence of charge patches, net charge of the particle, the ratio of positive to negative charges on the proteins on the net adsorption, and bridging probabilities of polyelectrolytes. Our results demonstrate that charge regulation increases the probability of bridging between two particles when compared to proteins with the same fixed charge. The influence of charge regulation first increases and then decreases with an increase in the number of charge patches of proteins. An increase in the ratio of positive to negative charges and the net charge of the protein are also seen to increase the propensity for polyelectrolyte adsorption and bridging.