<p>We investigate the two- and many-body physics of ultracold polar molecules dressed by dual microwaves with distinct polarizations. Using Floquet theory and multichannel scattering calculations, we identify a regime with the largest elastic-to-inelastic scattering ratio, which is favorable for performing evaporative cooling. Furthermore, we derive and subsequently validate an effective interaction potential that accurately captures the dynamics of microwave-shielded polar molecules (MSPMs). We also explore the ground-state properties of the ultracold gases of MSPMs by computing physical quantities such as gas density, condensate fraction, momentum distribution, and second-order correlation. It is shown that the system supports a weakly correlated expanding gas state and a strongly correlated self-bound gas state. Since the dual-microwave scheme introduces an additional control knob and is essential for creating ultracold Bose gases of polar molecules, our work pave the way for studying the two- and many-body physics of the ultracold polar molecules dressed by dual microwaves.</p>