A bootstrap methodology suitable for use with stationary and non‐stationary fractionally integrated time series is further developed in this article. The resampling algorithm involves estimating the degree of fractional integration, applying the fractional differencing operator, resampling the resulting approximation to the underlying short memory series and, finally, cumulating to obtain a resample of the original fractionally integrated process. This approach extends existing methods in the literature by allowing for general bootstrap schemes including blockwise bootstraps. Furthermore, we show that it can also be validly used for non‐stationary fractionally integrated processes. We establish asymptotic validity results for the general method and provide simulation evidence which highlights a number of favourable aspects of its finite sample performance, relative to other commonly used bootstrap methods.