The purpose of this paper is to investigate the bounds of the spectral norms of r-circulant and geometric circulant matrices whose elements are a generalization of Jacobsthal-Lucas numbers called bi-periodic Jacobsthal-Lucas numbers by three different ways. We also present the sum of entries; the maximum column sum matrix norm and the maximum row sum matrix norm of this circulant matrices. Then, we present bounds for the spectral norms of Kronecker and Hadamard products of r-circulant matrices and geometric circulant matrices with bi-periodic Jacobsthal-Lucas numbers. Finally, we give an explicit formula for the eigenvalues of r-circulant matrix with the bi-periodic Jacobsthal-Lucas numbers.