Theoretical uncertainties in the calculation of single inclusive b-quark and B-meson cross sections at high-energy <p(p)over bar> colliders and the agreement between new experimental data and theory are studied in detail taking into account recent results on alpha(s)(M(z)). Possible implications for the gluon distribution g(x,mu(2)) in the proton are discussed. The need for high-energy resummation techniques is examined by analysing the perturbative stability of the cross sections. For completeness, results for total <t(t)over bar> pair production are briefly presented.