  We study the ground state phase diagram of the bilayer Heisenberg model on
square lattice with a Bosonic RVB wave function. The wave function has the form
of a Gutzwiller projected Schwinger Boson mean field ground state and involves
two variational parameters. We find the wave function provides an accurate
description of the system on both sides of the quantum phase transition.
Especially, through the analysis of the spin structure factor, ground state
fidelity susceptibility and the Binder moment ratio $Q_{2}$, a continuous
transition from the antiferromagnetic ordered state to the quantum disordered
state is found at the critical coupling of
$\alpha_{c}=J_{\perp}/J_{\parallel}\approx2.62$, in good agreement with the
result of quantum Monte Carlo simulation. The critical exponent estimated from
the finite size scaling analysis($1/\nu\approx1.4$) is consistent with that of
the classical 3D Heisenberg universality class.
