How can the success of Bayesian models be reconciled with demonstrations of heuristic and biased reasoning?
Your question is predicated on the assumption that Bayesian modeling has been successful in all domains. I think this is a stance that many (except hardened Bayesians) would disagree with. For instance, consider the classic Tversky &amp; Shafir experiments on the violation of the sure thing principle:

What are popular rationalist responses to Tversky &amp; Shafir?

The above approach can be reconciled with standard rationalism, but you are in fact building theories of heuristics-and-biases to do so; that is how Kahneman &amp; Tversky arrived at their models. Similarly, you can build very awkward Bayesian models for these sort of tasks (other difficult tasks are ones that show an order effect) but it is hard to say how these models are different from heuristics. For a more general treatement:

What tasks does Bayesian decision-making model poorly?

However, in the domain where Bayesian modeling is a good fit, the reason it works well to reconcile with heuristics-and-biases is because it has the perfect mechanism for modeling bias: the initial prior distribution. In fact you can use the prior distribution in the bayesian approach to quantify bias.

To summarize, you can model heuristics-and-biases with the bayesian approach. For bayesians heuristics are how the task is modeled/represented and biases are the intial prior distributions