This study proposes a novel Bootstrap Combination method (BootComb) for estimating the long-memory parameter in stationary time series. We combine multiple bootstrap techniques to leverage their individual strengths and mitigate their weaknesses. Through extensive Monte Carlo simulations, we evaluate BootComb against individual bootstrap methods. Results demonstrate that BootComb consistently outperforms single bootstrap methods, with simpler combination strategies performing comparably to complex weighted schemes. BootComb also exhibits reduced bias variability. These findings suggest that combining bootstrap estimators can significantly enhance the accuracy and reliability of long-memory parameter estimation.