We present astrometric monitoring of the young exoplanet HD 95086 b obtained with the Gemini Planet Imager between 2013 and 2016. A small but significant position angle change is detected at constant separation; the orbital motion is confirmed with literature measurements. Efficient Monte Carlo techniques place preliminary constraints on the orbital parameters of HD 95086 b. With 68% confidence, a semimajor axis of 61.7(-8.4)(+20.7) au and an inclination of. 153.0(+9.7)(-13.5) are favored, with eccentricity less than 0.21. Under the assumption of a coplanar planet-disk system, the periastron of HD 95086 b is beyond 51 au with 68% confidence. Therefore, HD 95086 b cannot carve the entire gap inferred from the measured infrared excess in the SED of HD 95086. We use our sensitivity to additional planets to discuss specific scenarios presented in the literature to explain the geometry of the debris belts. We suggest that either two planets on moderately eccentric orbits or three to four planets with inhomogeneous masses and orbital properties are possible. The sensitivity to additional planetary companions within the observations presented in this study can be used to help further constrain future dynamical simulations of the planet-disk system.