We consider Zeeman field effects on a spin Bose-metal ͑SBM͒ phase on a two-leg triangular ladder. This phase was found in a spin-1/2 model with ring exchanges ͓D. N. Sheng, O. I. Motrunich, and M. P. A. Fisher, Phys. Rev. B 79, 205112 ͑2009͔͒ and was also proposed to appear in an interacting electronic model with longer-ranged repulsion ͓H.-H. Lai and O. I. Motrunich, Phys. Rev. B 81, 045105 ͑2010͔͒. Using bosonization of a spinon-gauge theory, we study the stability of the SBM phase and its properties under the field. We also explore phases arising from potential instabilities of the SBM; in all cases, we find a gap to spin-1 excitations while spin-nematic correlations are power law. We discuss two-dimensional analogues of these phases where spinons can pair with their own species.