We propose a bootstrap method for approximating the long-range terms in the contractor renormalization method. The idea is tested on the two-dimensional Heisenberg antiferromagnet and the frustrated ${J}_{2}\text{\ensuremath{-}}{J}_{1}$ model. We obtain renormalization group flows that directly reveal the N\'eel phase of the unfrustrated Heisenberg antiferromagnet and the existence of a phase transition in the ${J}_{2}\text{\ensuremath{-}}{J}_{1}$ model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.