We propose the inclusive semi-hard production, in proton-proton collisions, of two bottom-flavored hadrons, as well as of a single bottom-flavored hadron accompanied by a light jet, as novel channels for the manifestation of stabilization effects of the high-energy resummation under next-to-leading-order corrections. Our formalism relies on a hybrid high-energy and collinear factorization, where the BFKL resummation of leading and next-to-leading energy logarithms is used together with collinear factorization. We present results for cross sections and azimuthal correlations differential in rapidity, which are widely recognized as standard observables where to hunt for distinctive signals of the BFKL dynamics. We propose the study of double differential distributions in the transverse momenta of final-state particles as a common basis to investigate the interplay of different kinds of resummation mechanisms.