People's risk estimates often do not align with the evidence available to them. In particular, people tend to discount bad news (such as evidence suggesting their risk of being involved in a car accident is higher than they thought) as compared to good news (evidence suggesting it is lower) – this is known as the belief update bias. It has been assumed that individuals use motivated reasoning to rationalise away unwanted evidence (e.g., “I am a safe driver, thus these statistics do not apply to me”). However, whether reasoning is required to discount bad news has not been tested directly. Here, we restrict cognitive resources using a cognitive load (Experiment 1) and a time restriction manipulation (Experiment 3) and find that while these manipulations diminish learning in general, they do not diminish the bias. Furthermore, we also show that the relative neglect of bad news happens the moment new evidence is presented, not when participants are subsequently prompted to state their belief (Experiment 2). Our findings suggest that reasoning is not required for bad news to be discounted as compared to good news.