It might help if you told us which of the thousands of varieties of Bayesianism you have in mind with your question. (I would link to I.J. Good's letter on the 46656 Varieties of Bayesians, but the best I could come up with was the citation in Google Scholar, which does not make the actual text available.)

In terms of pure (or mostly pure) criticisms of frequentist interpretations of probability, you might look at two papers by Alan Hajek: fifteen arguments against finite frequentism and fifteen arguments against hypothetical frequentism.

In terms of Bayesian statistics, you might take a look at a couple of papers by Dennis Lindley: an older paper on The Present Position in Bayesian Statistics and a newer one on The Philosophy of Statistics.

Lindley gives a personalist Bayesian account. If you want "objective Bayes," you might take a look at this paper by James Berger. (The link actually has a bunch of papers, some of them discussing Berger's paper, which is the first in the set.)

You might also find Bradley Efron's paper Why Isn't Everyone a Bayesian? useful. And on that note, I'll just say that the presupposition of your question (that Bayesianism is straightforwardly superior to frequentism in all or most all cases) is more fraught than you might think.