We present the POL-2 850 μm linear polarization map of the Barnard 1 clump in the Perseus molecular cloud complex from the B-fields In STar-forming Region Observations survey at the James Clerk Maxwell Telescope. We find a trend of decreasing polarization fraction as a function of total intensity, which we link to depolarization effects toward higher-density regions of the cloud. We then use the polarization data at 850 μm to infer the plane-of-sky orientation of the large-scale magnetic field in Barnard 1. This magnetic field runs north-south across most of the cloud, with the exception of B1-c, where it turns more east-west. From the dispersion of polarization angles, we calculate a turbulence correlation length of 5.0 ±2.″5 (1500 au) and a turbulent-to-total magnetic energy ratio of 0.5 ±0.3 inside the cloud. We combine this turbulent-to-total magnetic energy ratio with observations of NH3 molecular lines from the Green Bank Ammonia Survey to estimate the strength of the plane-of-sky component of the magnetic field through the Davis-Chandrasekhar-Fermi method. With a plane-of-sky amplitude of 120 ±60 μG and a criticality criterion λ c = 3.0 ±1.5, we find that Barnard 1 is a supercritical molecular cloud with a magnetic field nearly dominated by its turbulent component.