We propose RemixIT, a simple and novel self-supervised training method for speech enhancement. The proposed method is based on a continuously self-training scheme that overcomes limitations from previous studies including assumptions for the in-domain noise distribution and having access to clean target signals. Specifically, a separation teacher model is pre-trained on an out-of-domain dataset and is used to infer estimated target signals for a batch of in-domain mixtures. Next, we bootstrap the mixing process by generating artificial mixtures using permuted estimated clean and noise signals. Finally, the student model is trained using the permuted estimated sources as targets while we periodically update teacher's weights using the latest student model. Our experiments show that RemixIT outperforms several previous state-of-the-art self-supervised methods under multiple speech enhancement tasks. Additionally, RemixIT provides a seamless alternative for semi-supervised and unsupervised domain adaptation for speech enhancement tasks, while being general enough to be applied to any separation task and paired with any separation model.