  We examine the potential of polarization bispectra of the cosmic microwave
background (CMB) to constrain primordial magnetic fields (PMFs). We compute all
possible bispectra between temperature and polarization anisotropies sourced by
PMFs and show that they are weakly correlated with well-known local-type and
secondary ISW-lensing bispectra. From a Fisher analysis it is found that, owing
to E-mode bispectra, in a cosmic-variance-limited experiment the expected
uncertainty in the amplitude of magnetized bispectra is 80% improved in
comparison with an analysis in terms of temperature auto-bispectrum alone. In
the $\mathit{Planck}$ or the proposed PRISM experiment cases, we will be able
to measure PMFs with strength 2.6 or 2.2 nG. PMFs also generate bispectra
involving B-mode polarization, due to tensor-mode dependence. We also find that
the B-mode bispectrum can reduce the uncertainty more drastically and hence
PMFs comparable to or less than 1 nG may be measured in a PRISM-like
experiment.
