The JWST discovery of "little red dots" (LRDs) is reshaping our picture of the early Universe, yet the physical mechanisms driving their compact size and UV-optical colors remain elusive. Here, we report an unusually bright LRD (zspec = 3.1) observed as part of the RUBIES program. This LRD exhibits broad emission lines (FWHM similar to 4000 km s-1), a blue UV continuum, a clear Balmer break, and a red continuum sampled out to rest-frame 4 mu m with MIRI. We develop a new joint galaxy and active galactic nucleus (AGN) model within the Prospector Bayesian inference framework and perform spectrophotometric modeling using NIRCam, MIRI, and NIRSpec/Prism observations. Our fiducial model reveals a M* similar to 109 M circle dot galaxy alongside a dust-reddened AGN driving the optical emission. Explaining the rest-frame optical color as a reddened AGN requires AV greater than or similar to 3, suggesting that a great majority of the accretion disk energy is reradiated as dust emission. Yet, despite clear AGN signatures, we find a surprising lack of hot torus emission, which implies that either the dust emission in this object must be cold, or the red continuum must instead be driven by a massive, evolved stellar population of the host galaxy-seemingly inconsistent with the high-EW broad lines (H alpha rest-frame EW similar to 800 & Aring;). The widths and luminosities of Pa-beta, Pa-delta, Pa-gamma, and H alpha imply a modest black hole mass of MBH similar to 108 M circle dot. Additionally, we identify a narrow blueshifted He i lambda 1.083 mu m absorption feature in NIRSpec/G395M spectra, signaling an ionized outflow with kinetic energy up to similar to 1% the luminosity of the AGN. The low redshift of RUBIES-BLAGN-1, combined with the depth and richness of the JWST imaging and spectroscopic observations, provides a unique opportunity to build a physical model for these so-far mysterious LRDs, which may prove to be a crucial phase in the early formation of massive galaxies and their supermassive black holes.