  We consider Zeeman field effects on a Spin Bose-Metal (SBM) phase on a
two-leg triangular ladder. This phase was found in a spin-1/2 model with ring
exchanges [D. N. Sheng et. al., Phys. Rev. B {\bf 79}, 205112 (2009)], and was
also proposed to appear in an interacting electronic model with longer-ranged
repulsion [Lai et. al., Phys. Rev. B {\bf 81}, 045105 (2010)]. 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.
