The redshift space anisotropy of the bispectrum is generally quantified using
multipole moments. The possibility of measuring these multipoles in any survey
depends on the level of statistical fluctuations. We present a formalism to
compute the statistical fluctuations in the measurement of bispectrum
multipoles for galaxy surveys. We consider specifications of a {\it Euclid}
like galaxy survey and present two quantities: the signal-to-noise ratio (SNR)
which quantifies the detectability of a multipole, and the rank correlation
which quantifies the correlation in measurement errors between any two
multipoles. Based on SNR values, we find that {\it Euclid} can potentially
measure the bispectrum multipoles up to $\ell =4$ across various triangle
shapes, formed by the three {\bf k} vectors in Fourier space. In general, SNR
is maximum for the linear triangles. SNR values also depend on the scales and
redshifts of observation. While, $\ell \le 2$ multipoles can be measured with
$\mathrm{S}\mathrm{N}\mathrm{R}>5$ even at linear/quasi-linear ($k\lesssim 0.1{\textstyle \phantom{\rule{0.167em}{0ex}}}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$ )
scales, for $\ell >2$ multipoles, we require to go to small scales or need to
increase bin sizes. For most multipole pairs, the errors are only weakly
correlated across much of the triangle shapes barring a few in the vicinity of
squeezed and stretched triangles. This makes it possible to combine the
measurements of different multipoles to increase the effective SNR.