In a vast body of opinion dynamics literature, an agent updates its opinion based on the opinions of its neighbors in a static social graph, regardless of their differences in opinions. In contrast, the bounded confidence opinion dynamics does not presume a static interaction graph, and instead limits interactions to those agents that share related opinions (i.e., whose opinions are close to one another). We generalize the bounded confidence opinion dynamics model by incorporating stochastic interactions based on opinion differences and the endogenous evolution of the agent opinions, which itself is a random process. We analytically characterize the conditions under which this stochastic dynamics is stable in an appropriate sense.