One of the core challenges in Visual Dialogue problems is asking the question that will provide the most useful information towards achieving the required objective. Encouraging an agent to ask the right questions is difficult because we don't know a-priori what information the agent will need to achieve its task, and we don't have an explicit model of what it knows already. We propose a solution to this problem based on a Bayesian model of the uncertainty in the implicit model maintained by the visual dialogue agent, and in the function used to select an appropriate output. By selecting the question that minimises the predicted regret with respect to this implicit model the agent actively reduces ambiguity. The Bayesian model of uncertainty also enables a principled method for identifying when enough information has been acquired, and an action should be selected. We evaluate our approach on two goal-oriented dialogue datasets, one for visual-based collaboration task and the other for a negotiation-based task. Our uncertainty-aware information-seeking model outperforms its counterparts in these two challenging problems.