Agreed--in fact, science doesn't rely on philosophy at all. If the entire field of philosophy disappeared, science would go on functioning just fine. In fact, science has generally been hindered by philosophy--it's seemingly impossible to discuss scientific methodology without some wanker interjecting "well ackchyually nothing is knowable". Animals with nervous systems were learning from observation before humans invented enough language to epistemologize, and will continue to do so with or without philosophers.
Bayesian epistemology is an attempt to model why science works--it relies on science, not the other way around.
Bayesian epistemology is not used in almost any domain in science, it does not model why science works, and it does not rely on science: it relies on metaphysics.
The scientific method may at one time have been conceived by philosophers, but we are centuries away from that time, and in recent centuries, all the refinements and improvements to science have been done by scientists. The roots of the scientific method which one could reasonably call philosophy are so changed as to be considered invalid today.
The reverse is not true--scientists have written a lot of philosophy--and since they tend to base their philosophy in reality rather than logic based on speculation, it tends to be better philosophy than philosophers.
Bayesian epistemology is an attempt to model why science works--it relies on science, not the other way around.