We extend our previous analysis on inclusive heavy quarkonia hadroproduction to the whole Upsilon(nS) (n=1,2,3) resonance family. We use a Monte Carlo framework with the colour-octet mechanism implemented in the PYTHIA event generator. We include in our study higher order QCD effects such as initial-state emission of gluons and Altarelli-Parisi evolution of final-state gluons. We extract some NRQCD colour-octet matrix elements relevant for Upsilon(nS) (n=1,2,3) hadroproduction from CDF data at the Fermilab Tevatron. Then we extrapolate to LHC energies to predict prompt bottomonia production rates. Finally, we examine the prospect to probe the gluon density in protons from heavy quarkonia inclusive hadroproduction at high transverse momentum and its feasibility in LHC general-purpose experiments.