Presentability of categories of localizations and analytic rings

We prove that certain categories of Bousfield localizations are presentable and give explicit regular cardinals $\kappa$ for which they are $\kappa$-presentable. As an application, we show that the category of analytic rings in the sense of Clausen and Scholze is $(2^{{\mathrm{\aleph }}_0}{)}^{+}$-presentable.