This may be nitpicking and I agree with your overarching point, but I think you're drawing a false dichotomy between Science and Bayes. Science is the process of constructing theories to explain data. The theory must optimize a tradeoff between two terms:

1) ability to explain data 2) compactness of the theory

If one is willing to ignore or gloss over the second requirement, the process becomes nonsense. One can easily construct a theory of astrology which explains the motion of the planets, the weather, the fates of lovers, and violence in the Middle East. It just won't be a compact theory. So Science and Bayes are one and the same.