Protein expression in a single cell depends on its global physiological state. Moreover, genetically-identical cells exhibit variability (noise) in protein expression, arising from the stochastic nature of biochemical processes, cell growth and division. While it is well understood how cellular growth rate influences mean protein expression, little is known about the relationship between growth rate and noise in protein expression. Here we quantify this relationship in Bacillus subtilis by a novel combination of experiments and theory. We measure the effects of promoter activity and growth rate on the expression of a fluorescent protein in single cells. We disentangle the observed protein expression noise into protein-specific and systemic contributions, using theory and variance decomposition. We find that noise in protein expression depends solely on mean expression levels, regardless of whether expression is set by promoter activity or growth rate, and that noise increases linearly with growth rate. Our results can aid studies of (synthetic) gene circuits of single cells and their condition dependence.