Automatic post-editing (APE) seeks to automatically refine the output of a black-box machine translation (MT) system through human post-edits. APE systems are usually trained by complementing human post-edited data with large, artificial data generated through back-translations, a time-consuming process often no easier than training a MT system from scratch. in this paper, we propose an alternative where we fine-tune pre-trained BERT models on both the encoder and decoder of an APE system, exploring several parameter sharing strategies. By only training on a dataset of 23 K sentences for 3 hours on a single GPU we obtain results that are competitive with systems that were trained on 5 M artificial sentences. When we add this artificial data our method obtains state-of-the-art results.