Because in all the case that I know, either a Bayesian model can be reduced to a frequentist one or a Bayesian model gives more accurate prediction.

I typically see this stated as "there is a Bayesian interpretation for every effective statistical technique." As pointed out elsewhere, typically people use "frequentist" to mean "non-Bayesian," which is not particularly effective as a classification.

So I'm asking "is there a book that teaches ML from a Bayesian point of view?".

The answer I'm discovering, appallingly but maybe not so, is no.

Did you google Bayesian Machine Learning, or search for it on Amazon? Barber is a well-rated textbook available online for free. (I haven't read it; Sebastien Bratieres thinks it's comparable to Murphy, the second most popular ML book, which is Bayesian.) Incidentally, Bishop, the most popular ML book, is also Bayesian. You managed to find the only ML textbook I've seen which has, as a comment in one of the Amazon reviews, a positive comment that the book is not Bayesian!

The more meta point here is to not let a worldview shut you out from potentially useful resources. Yes, Bayesianism is the best philosophy of probability, but that does not mean it is the most effective practice of statistics, and excluding concepts or practices from your knowledge of statistics because of a disagreement on philosophy is parochial and self-limiting.