We investigate the prospects for heavy charged Higgs boson production through the mechanisms pp-bar(pp)->tbH+ +X at the upgraded Fermilab Tevatron and at the upcoming LHC collider at CERN respectively. We focus on the MSSM case at high values of tan[beta]> m_top/m_bot and include the leading SUSY quantum corrections. A detailed study is performed for all important production modes and basic background processes for the "ttbb" signature. At the upgraded Tevatron a charged Higgs signal is potentially viable in the 220-250 GeV range or excluded at 95%CL up to 300 GeV. At the LHC, a H+ of mass up to 800 GeV can be discovered at 5 sigma or else be excluded up to a mass of ~ 1.5 TeV. The presence ofSUSY quantum effects may highly influence the discovery potential in both machines and can typically shift these limits by 200 GeV at the LHC.