When randomized ensemble methods such as bagging and random forests are\nimplemented, a basic question arises: Is the ensemble large enough? In\nparticular, the practitioner desires a rigorous guarantee that a given ensemble\nwill perform nearly as well as an ideal infinite ensemble (trained on the same\ndata). The purpose of the current paper is to develop a bootstrap method for\nsolving this problem in the context of regression --- which complements our\ncompanion paper in the context of classification (Lopes 2019). In contrast to\nthe classification setting, the current paper shows that theoretical guarantees\nfor the proposed bootstrap can be established under much weaker assumptions. In\naddition, we illustrate the flexibility of the method by showing how it can be\nadapted to measure algorithmic convergence for variable selection. Lastly, we\nprovide numerical results demonstrating that the method works well in a range\nof situations.\n