In this paper, we discuss the importance of modeling the potential bother to the user, when reasoning about interaction in a mixed-initiative setting. We summarize our previous work on modeling bother as one of the costs of interaction, clarifying how to incorporate this estimated cost when reasoning about whether to initiate interaction. We then present a new method for modeling bother that appeals to classifications of users according to their willingness and attentional state and attaches a level of bother to the kind of task being asked of the user, when interacting. We demonstrate the usefulness of this model in the context of a multiagent system, where each agent faces the challenge of estimating the bother incurred by a user as a result of interactions from other agents. This is accomplished by the introduction of proxy agents for each user, to track the requests for interaction from multiple parties. We discuss the trade-off between more accurate bother cost information and higher communication overhead, when reasoning about whether to initiate interactions with users, as part of the collaborative problem solving. Our conclusion is that bother is indeed important to model and that it is in fact possible to effectively integrate consideration of bother cost into methods for reasoning about interaction with users.