The ability to update the structure of a Bayesian network when new data becomes available is crucial for building adaptive systems. Recent work by Sang, Beame, and Kautz (AAAI 2005) demonstrates that the well-known Davis-Putnam procedure combined with a dynamic decomposition and caching technique is an effective method for exact inference in Bayesian networks with high density and width. In this paper, we define dynamic model counting and extend the dynamic decomposition and caching technique to multiple runs on a series of problems with similar structure. This allows us to perform Bayesian inference incrementally as the structure of the network changes. Experimental results show that our approach yields significant improvements over the previous model counting approaches on multiple challenging Bayesian network instances.