Causal mediation analysis is a popular tool for studying complicated causal dependence between multiple variables. The main question we want to answer is to what extent the effect of an exposure, X, on a response, Y, is mediated by a third variable, M. One common approach involves fitting some regression models and computing simple, albeit non-linear, functions of the estimated coefficients. Uncertainty quantification for these "mediation effects" is non-trivial in even the simplest settings, with published simulation studies finding that asymptotic standard errors obtained from the delta method often perform poorly in finite samples. A popular alternative to these analytical standard error formulas is to use the bootstrap, a computational tool which involves using repeated draws from an approximate sampling distribution to assess the standard error of a statistic. We present a range of implementations for the bootstrap on a complicated statistical model involving non-linearity and mixed-effects, and illustrate our analysis on a dataset investigating the relationship between trustworthiness of peoples' preferred news source and willingness to adhere to pandemic lockdown mandates.