This is an active area of research in the cognitive science world.
First, 'bias' is defined with respect to an ideal rational actor with perfect information and infinite computing power. The reasons for this are mostly historical (rational animal, Homo economicus, etc), but it also serves as a useful baseline 'ideal observer' model to compare human behavior against.
In the 1950s, Herbert Simon coined the term 'bounded rationality' to describe rationality within a set of computational bounds. For example, if we have finite working memory and limited computing time, but were still trying to make optimal decisions within those bounds, what behavior would we see? In this case, decision making turns from unconstrained to constrained optimization. What may LOOK like a 'bias', with its connotation of sub-optimality, may actually be optimal behavior given constraints.
More recently, people like Gerd Gigerenzer suggested that human decision making is largely composed of heuristics and tricks that enable 'fast and frugal' responses to scenarios. They don't need to be perfect, just good enough - and 'cheap' enough with respect to time that they are worth developing. This is probably true to a certain extent, but to me it's scientifically unsatisfying, as there is no general principle (except for 'cognitive miserliness') to explain behavior - and specifically, there is no longer a way to specify 'normative' or expected behavior in any given situation.
More recently still, there is a trend to revive Simon's perspective under the name 'Resource Rationality'. Tom Griffiths is one of the active researchers in this field. The idea is the similar to Simon's - we have limited 'cognitive resources' and strive to be rational. Griffiths and others have attempted to show that many behaviors that are traditionally called 'cognitive biases' are actually predicted if we are behaving optimally but with constrained cognitive resources.
From the resource rationality perspective, a cognitive bias is a way that a solution to unconstrained optimization differs from a solution to a corresponding constrained optimization problem. Roughly speaking, any combination of limitation on (memory, computation, time, energy, information) will produce a 'bias', and different scenarios we encounter push up against these boundaries in different ways, leading to a plethora of 'biases'.