Bessel filter second-order sections Q and Fc multiplier derivation
There is no simple closed-form equation to calculate Bessel filter bi-quad coefficients. The poles of the filter come from a Bessel polynomial. Higher order Bessel polynomials are determined using a recursion relationship. You need computer algorithms to calculate the poles and resolve the bi-quad coefficients. 

Two books I can recommend: “Passive and Active Filters” by Wai-Kai Chen and “Analog Filter Design” by M.E. Van Valkenburg.