Multiple-timepoint arterial spin labelling MRI is a non-invasive imaging technique that permits measurement of both cerebral blood flow and arterial transit time, the latter of which is an emerging biomarker of interest for cerebrovascular health. Quantification of arterial spin labelling data is challenging due to the low signal to noise ratio and non-linear tracer kinetics of this technique. In this work, we introduce a new quantification method called SSVB that addresses limitations in existing methods and demonstrate its performance using simulations and acquisition data. Simulations showed that the method is more accurate, particularly for estimating arterial transit time, and more robust to noise than existing techniques. On high spatial resolution data acquired at 3 T, the method produced less noisy parameter maps than the comparator method and captured greater variation in arterial transit time on a cross-sectional cohort.