The boron isotope ratio of seawater (δ11Bsw) is a parameter which must be known to reconstruct palaeo pH and CO2 from boron isotope measurements of marine carbonates. Beyond a few million years ago, δ11Bsw is likely to have been different to modern. Palaeo δ11Bsw can be estimated by simultaneously constraining the vertical gradients in foraminiferal δ11B (∆δ11B) and pH (∆pH). A number of subtly different techniques have been used to estimate ∆pH in the past, all broadly based on assumptions about vertical gradients in oxygen, and/or carbon, or other carbonate system constraints. In this work we pull together existing data estimates alongside limitations on the rate of change of δ11Bsw from modelling, and combine these into an overarching statistical framework called a Gaussian Process. The Gaussian Process technique allows us to bring together data and constraints on the rate of change in δ11Bsw to generate random plausible evolutions of δ11Bsw. We reconstruct δ11Bsw, and by extension palaeo pH, across the last 65Myr using this novel methodology. Reconstructed δ11Bsw is compared to other seawater isotope ratios, namely 87/86Sr, 187/188Os, and δ7Li, which we also reconstruct with Gaussian Processes. Our method provides a template for incorporation of future δ11Bsw constraints, and a mechanism for propagation of uncertainty in δ11Bsw into future studies.