We present a 3D map of magnetic field orientation on the surface of the Local Bubble. This map is the first of its kind to fully chart magnetic fields over an observed superbubble. Recent work mapping the 3D shape and dynamics of the Local Bubble has revealed that the formation of all young stars within 200 pc of the Sun was triggered by the Bubble's rapid expansion. The exact mechanics of this expansion, and the role that magnetic fields in the surrounding interstellar medium have played in regulating its evolution, is not yet clear. By combining detailed models of the Bubble’s geometry (derived from 3D dust mapping) with the assumption that magnetic field vectors are tangent to the Bubble’s surface, we are able to infer the 3D magnetic field orientation from Planck plane-of-the-sky dust polarization orientations. We analyze the relationship between the Bubble’s inferred magnetic field and background starlight polarimetry observations, and discuss how magnetic fields may have affected the dynamics of the Local Bubble and other nearby structures in the ISM.