This paper considers bootstrap inference in a factor-augmented regression context where the errors could potentially be serially correlated. This generalizes results in Gonçalves and Perron (2013) and makes the bootstrap applicable to forecasting contexts where the forecast horizon is greater than one. We propose and justify two residual-based approaches, a block wild bootstrap (BWB) and a dependent wild bootstrap (DWB). Our simulations document improvement in coverage rates of confidence intervals for the coefficients when using BWB or DWB relative to both asymptotic theory and the wild bootstrap when serial correlation is present in the regression errors.