  Upcoming galaxy surveys aim to map the Universe with unprecedented precision,
depth and sky coverage. The galaxy bispectrum is a prime source of information
as it allows us to probe primordial non-Gaussianity (PNG), a key factor in
differentiating various models of inflation. On the scales where local PNG is
strongest, Doppler and other relativistic effects become important and need to
be included. We investigate the detectability of relativistic and local PNG
contributions in the galaxy bispectrum. We compute the signal-to-noise ratio
for the detection of the bispectrum including such effects. Furthermore, we
perform information matrix forecasts on the local PNG parameter $f_{\rm NL}$
and on the parametrised amplitudes of the relativistic corrections. Finally, we
quantify the bias on the measurement of $f_{\rm NL}$ that arises from
neglecting relativistic effects. Our results show that detections of both
first- and second-order relativistic effects are promising with forthcoming
spectroscopic survey specifications -- and are largely unaffected by the
uncertainty in $f_{\rm NL}$. Conversely, we show for the first time that
neglecting relativistic corrections in the galaxy bispectrum can lead to
$>\!1.5\sigma(f_{\rm NL})$ shift on the detected value of $f_{\rm NL}$,
highlighting the importance of including relativistic effects in our modelling.
