Recent experimental evidence suggests the presence of an unconventional, nodal surface-superconducting state in trigonal PtBi₂. We construct a Ginzburg-Landau theory for the three superconducting order parameters, which correspond to the three irreducible representations of the point group C₃v. The irreducible representations A₁ and A₂ are the most likely. We develop a systematic method to determine the symmetry-allowed terms and apply it to derive all terms up to fourth order in the three order parameters. The Ginzburg-Landau functional also includes coupling to the magnetic field. The functional is employed to determine the effect of an applied uniform magnetic field on the nodal structure for A₁ and A₂ pairing. The results facilitate clear-cut experimental differentiation between these symmetries. We also predict field-induced helical superconductivity.