You can expand “Don’t worry about it” to include permission to bother her. “Don’t worry about it—please never give it a second thought if you need me for anything. That’s what I’m here to do.”
I don’t think “This doesn’t bother me” gets parsed literally anyway. In either case what ever you say they are pretty sure it is annoying for you, albeit they do want reassurance that it is not so annoying that you would snap “yes this is annoying!”.
You can expand “Don’t worry about it” to include permission to bother her. “Don’t worry about it—please never give it a second thought if you need me for anything. That’s what I’m here to do.”
I don’t think “This doesn’t bother me” gets parsed literally anyway. In either case what ever you say they are pretty sure it is annoying for you, albeit they do want reassurance that it is not so annoying that you would snap “yes this is annoying!”.