In this paper, we propose two Bregman regularized proximal point methods that provide flexibility to compute projected solutions for quasi-equilibrium problems. Each method has one Bregman projection onto the feasible set and the regularized equilibrium problem. Under standard assumptions, we prove that the methods are well-defined and that the sequences they generate converge to a projected solution of the quasi-equilibrium problem. Additionally, we prove that both methods attain an R-linear rate of convergence under the relatively strong monotonicity assumption. Furthermore, we perform numerical experiments on some test problems to illustrate the effectiveness of the proposed methods. The results obtained in this paper can be considered as the generalization and improvement of some existing works in the field of equilibrium and quasi-equilibrium problems.