You can't really disrupt a person. You can disrupt a meeting. Generally you would not ask permission before disrupting something and very often disruption is involuntary. If you interrupt someone, he must be in the process of doing something. Most commonly this is speaking. By asking someone can you interrupt him, you are asking him to stop speaking so that you may make a point which will affect what he is going to say. You can also interrupt other actions and things, e.g. a meeting. The difference between disruption and interruption is that it is implied that the meeting will continue once the interruption is over, whereas a disruption may end it. You can disturb someone who is not speaking. Generally you would say this to someone who is, for example, reading quietly, having a drink, working out etc .

All of these mean cause somebody/something to stop 1. Interrupt : especially when someone is speaking 2. Disturb : that will make someone upset or worried 3. Distupt : prevent an event/system...from continuing in a normal way