I'm afraid that is not a clear sentence.
So you want to set it up so that only the assignee can reassign an issue to someone else? Or do you mean you want to stop people assigning the issue to anyone but themselves?
I'm still not 100% sure I understand, but it sounds like what you want is to stop Bob reassigning the issue to someone else.
Have a look at the permission scheme - you need to modify it in a way that says "Bob is not included in the people who can assign issues in this project"
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