  A primordial cosmic microwave background B-mode is widely considered a
"smoking gun" signature of an early period of inflationary expansion. However,
competing theories of the origin of structure, including string gases and
bouncing cosmologies, also produce primordial tensor perturbations that give
rise to a B-mode. These models can be differentiated by the scale dependence of
their tensor spectra: inflation predicts a red tilt ($n_T<0$), string gases and
loop quantum cosmology predict a blue tilt ($n_T>0$), while a nonsingular
matter bounce gives zero tilt ($n_T=0$). We perform a Bayesian analysis to
determine how far $|n_T|$ must deviate from zero before a tilt can be detected
with current and future B-mode experiments. We find that Planck in conjunction
with QUIET (II) will decisively detect $n_T \neq 0$ if $|n_T| > 0.3$, too large
to distinguish either single field inflation or string gases from the case
$n_T=0$. While a future mission like CMBPol will offer improvement, only an
ideal satellite mission will be capable of providing sufficient Bayesian
evidence to distinguish between each model considered.
