State estimation methods based on hybrid discrete and continuous state models have emerged as a method of precisely computing belief states for real world systems, however they have difficulty scaling to systems with more than a handful of components. Classical, consistency based diagnosis methods scale to this level by combining best-first enumeration and conflict-directed search. While best-first methods have been developed for hybrid estimation, conflict-directed methods have thus far been elusive as conflicts summarize constraint violations, but probabilistic hybrid estimation is relatively unconstrained. In this paper we present an approach (A*BC) that unifies best-first enumeration and conflict-directed search in relatively unconstrained problems through the concept of "bounding" conflicts, an extension of conflicts that represent tighter bounds on the cost of regions of the search space. Experiments show that an A*BC powered state estimator produces estimates up to an order of magnitude faster than the current state of the art, particularly on large systems.