A physically realistic stellar wind model based on Alfven wave dissipation has been used to simulate the wind from Barnards Star and to estimate the conditions at the location of its recently discovered planetary companion. Such models require knowledge of the stellar surface magnetic field that is currently unknown for Barnards Star. We circumvent this by considering the observed field distributions of three different stars that constitute admissible magnetic proxies of this object. Under these considerations, Barnards Star b experiences less intense wind pressure than the much more close-in planet Proxima~b and the planets of the TRAPPIST-1 system. The milder wind conditions are more a result of its much greater orbital distance rather than in differences in the surface magnetic field strengths of the host stars. The dynamic pressure experienced by the planet is comparable to present-day Earth values, but it can undergo variations by factors of several during current sheet crossings in each orbit. The magnetospause standoff distance would be $sim$,$20 - 40$,% smaller than that of the Earth for an equivalent planetary magnetic field strength.
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