Bolus-tracking MRI involves the bolus injection of contrast agent, and the resultant concentration time course can be used to calculate perfusion by deconvolution analysis. However, most deconvolution methods do not provide a measure of precision. Precision could be estimated from many repeated measurements; however, this would involve a series of successive bolus injections, which is not a feasible option in practice due to contrast agent dose constraints. In this work, a method is presented to estimate precision in bolus-tracking MRI using the wild-bootstrap method. This approach is able to estimate the uncertainty in perfusion measurements from the data acquired during a single bolus of contrast agent injection. The methodology was assessed using numerical simulations and applied to real data with a range of image qualities. The method is shown to provide useful estimates of precision, and the results from real data were consistent with the underlying MRI data quality. The methodology provides an important complementary tool in clinical and research applications of bolus-tracking MRI.