Conversation forecasting tasks a model with predicting the outcome of an unfolding conversation. For instance, it can be applied in social media moderation to predict harmful user behaviors before they occur, allowing for preventative interventions. While large language models (LLMs) have recently been proposed as an effective tool for conversation forecasting, it's unclear what biases they may have, especially against forecasting the (potentially harmful) outcomes we request them to predict during moderation. This paper explores to what extent model uncertainty can be used as a tool to mitigate potential biases. Specifically, we ask three primary research questions: 1) how does LLM forecasting accuracy change when we ask models to represent their uncertainty; 2) how does LLM bias change when we ask models to represent their uncertainty; 3) how can we use uncertainty representations to reduce or completely mitigate biases without many training data points. We address these questions for 5 open-source language models tested on 2 datasets designed to evaluate conversation forecasting for social media moderation.