Environmental time-series data often exhibit gaps of varying lengths and frequencies, posing challenges in filling these gaps and understanding the uncertainty associated with the interpolation process, particularly when dealing with input-dependent noise. The heteroscedastic Gaussian process offers a promising solution by filling the gaps and providing input-dependent variance estimates. However, this method is typically designed to work efficiently when replicate observations are available for each unique design location, which may not always be the case. To address this limitation, we extended the Heteroscedastic Gaussian process of Binois and Gramacy [Binois et al., 2018] by incorporating a Block Bootstrap adjustment. This involved generating pseudo-replicates of time-series data that contain gaps. Through extensive Monte Carlo experiments, we tested the method with different variance surfaces, noise levels, and randomized gap sequences. The results demonstrate that our approach is both computationally efficient and flexible. The inclusion of user-defined parameters ensures the generation of more extreme or conservative variance estimates, accommodating different modeling requirements and preferences. Overall, our extended method offers an effective means of estimating variances in environmental time-series data, even in scenarios where replicates for each unique design location are not available.