Highly controlled Fe-catalyzed growth of monolayer hexagonal boron nitride (h-BN) films is demonstrated by the dissolution of nitrogen into the catalyst bulk via NH3 exposure prior to the actual growth step. This "pre-filling" of the catalyst bulk reservoir allows us to control and limit the uptake of B and N species during borazine exposure and thereby to control the incubation time and h-BN growth kinetics while also limiting the contribution of uncontrolled precipitation-driven h-BN growth during cooling. Using in situ X-ray diffraction and in situ X-ray photoelectron spectroscopy combined with systematic growth calibrations, we develop an understanding and framework for engineering the catalyst bulk reservoir to optimize the growth process, which is also relevant to other 2D materials and their heterostructures.