We propose new, data-efficient training tasks for BERT models that improve performance of automatic speech recognition (ASR) systems on conversational speech. We include past conversational context and fine-tune BERT on transcript disambiguation without external data to rescore ASR candidates. Our results show word error rate recoveries up to 37.2%. We test our methods in low-resource data domains, both in language (Norwegian), tone (spontaneous, conversational), and topics (parliament proceedings and customer service phone calls). These techniques are applicable to any ASR system and do not require any additional data, provided a pre-trained BERT model. We also show how the performance of our context-augmented rescoring methods strongly depends on the degree of spontaneity and nature of the conversation.