We present the POL-2 850 \mu m linear polarization map of the Barnard 1 clump in the Perseus molecular cloud complex from the B-fields In STar-forming Region Observations ( BISTRO ) 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 towards higher density regions of the cloud . We then use the polarization data at 850 \mu m 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 \pm 2.5 arcsec ( 1500 au ) , and a turbulent-to-total magnetic energy ratio of 0.5 \pm 0.3 inside the cloud . We combine this turbulent-to-total magnetic energy ratio with observations of NH _ { 3 } molecular lines from the Green Bank Ammonia Survey ( GAS ) 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 \pm 60 \mu G and a criticality criterion \lambda _ { c } = 3.0 \pm 1.5 , we find that Barnard 1 is a supercritical molecular cloud with a magnetic field nearly dominated by its turbulent component .