Using your geometric analogy, science is the process of sketching a circle, while Bayesian reasoning is a compass.

To continue the metaphor: science is the system of reasoning we use to recognize that the compass will make approximate circles, figure out how to build compasses, and recommend that people use them when they want to draw a circle.

As a system, Bayesian reasoning it is sufficiently broad and flexible that it can be used to represent more sophisicated forms of reasoning, in the same way that everyday language can represent formal logic. But as common speech is less powerful than the restricted language of logic, Bayesianism is less powerful than reasoning with tighter standards of evidence.

It is useful to look back into the primitive roots of thought. But we developed more complex tools for a reason.