  Unconventional superconductivity typically emerges in the presence of
quasi-degenerate ground states, and the associated intense fluctuations are
likely responsible for generating the superconducting state. Here we use
polarized neutron scattering to study the spin space anisotropy of spin
excitations in Fe$_{1.07}$Te exhibiting bicollinear antiferromagnetic (AF)
order, the parent compound of FeTe$_{1-x}$Se$_x$ superconductors. We confirm
that the low energy spin excitations are transverse spin waves, consistent with
a local-moment origin of the bicollinear AF order. While the ordered moments
lie in the $ab$-plane in Fe$_{1.07}$Te, it takes less energy for them to
fluctuate out-of-plane, similar to BaFe$_2$As$_2$ and NaFeAs. At energies above
$E\gtrsim20$ meV, we find magnetic scattering to be dominated by an isotropic
continuum that persists up to at least 50 meV. Although the isotropic spin
excitations cannot be ascribed to spin waves from a long-range ordered local
moment antiferromagnet, the continuum can result from the bicollinear magnetic
order ground state of Fe$_{1.07}$Te being quasi-degenerate with plaquette
magnetic order.
