Topologically non-trivial surface states were reported first on ${\mathrm{Bi}}_{1-x}$Sb x bulk crystals. In this study we present transport measurements performed on thin ${\mathrm{Bi}}_{1-x}$Sb x -films (up to 24 nm thickness) grown epitaxially on Si(111) with various Sb-concentrations (up to x = 0.22). The analysis of the temperature dependency allowed us to distinguish between different transport channels originating from surface and bulk bands as well as impurity states. At temperatures below 30 K the transport is mediated by surface states while at higher temperatures activated transport via bulk channels sets in. The surface state conductivity and bulk band gaps can be tuned by the Sb-concentration and film thickness, respectively. For films as thin as 4 nm the surface state transport is strongly suppressed in contrast to Bi(111) films grown under identical conditions. The impurity channel is of intrinsic origin due to the growth and alloy formation process and turns out to be located at the buried interface.