A 28 GHz system with a high-power gyrotron tube has been used for the QUEST spherical tokamak to form an over-dense plasma for electron Bernstein wave (EBW) heating and current drive with an 8.2 GHz-wave. Non-inductive high-density plasma ramp-up experiments with dual-frequency (dual-f) electron cyclotron (EC) (8.2 GHz and 28 GHz) waves were conducted. A spontaneous density jump (SDJ) to an over-dense state was first observed as a bifurcation phenomenon in the dual-f wave experiment. The over-dense plasma on the 8.2 GHz wave was non-inductively ramped up to 25 kA, and was maintained for 0.4 s under stable plasma equilibrium after two such jumps in one shot. Heating to mildly energetic electrons and bulk electrons was observed even in the over-dense region. The electrostatic EBW heating effect on the mildly energetic electrons in the over-dense region is assessed following a dispersion analysis of the 8.2 GHz wave. The bulk electron heating effect observed is explained as heat exchange from mildly energetic electrons heated by the electrostatic EBW. Remarkably, a high hard-x-ray-radiation temperature of similar to 500 keV was also observed in tangential viewing for current-carrying electrons in the over-dense core region. Synergetic heating from the overlap of different 28 GHz EC harmonic resonances as well as higher harmonic heating is discussed for maintaining the highly energetic electrons in the over-dense core region. In addition, the SDJ process and mechanism are considered based on the discussion of the electron heating effects with the 8.2 GHz wave.