Incorporation of Bi into GaAs-(Ga,Al)As-Ga(As,Bi) core-shell nanowires grown by molecular beam epitaxy is studied with transmission electron microscopy. Nanowires are grown on GaAs(111)B substrates with Au-droplet assisted mode. Bi-doped shells are grown at low temperature (300 degrees C) with a close to stoichiometric Ga/As flux ratio. At low Bi fluxes, the Ga(As,Bi) shells are smooth, with Bi completely incorporated into the shells. Higher Bi fluxes (Bi/As flux ratio similar to 4%) led to partial segregation of Bi as droplets on the nanowires sidewalls, preferentially located at the nanowire segments with wurtzite structure. We demonstrate that such Bi droplets on the sidewalls act as catalysts for the growth of branches perpendicular to the GaAs trunks. Due to the tunability between zinc-blende and wurtzite polytypes by changing the nanowire growth conditions, this effect enables fabrication of branched nanowire architectures with branches generated from selected (wurtzite) nanowire segments.