In this work, we study the interlayer interactions between sheets of blue phosphorus with quantum Monte Carlo (QMC) methods. We find that as previously observed in black phosphorus, interlayer binding of blue phosphorus cannot be described by van der Waals (vdW) interactions alone within the density functional theory framework. Specifically, while some vdW density functionals produced reasonable binding curves, none of them could provide a correct, even qualitatively, description of charge redistribution due to interlayer binding. We also show that small systematic errors in common practice QMC calculations, such as the choice of optimized geometry and finite-size corrections, are non-negligible given the energy and length scales of this problem. We mitigate some of the major sources of error and report QMC-optimized lattice constant, stacking, and interlayer binding energy for blue phosphorus. It is strongly suggested that these considerations are important and quite general in the modeling of two-dimensional phosphorus allotropes.