Is there a way to have 1 distribution list that has bursting values for some people, yet there is a person that actually needs the entire report. Or do I have to actually run the report twice and send it out one with bursting, one without?

If you have 1 person who gets cc'd on every instance of the burst value, that poor person will get a lot of separate emails.
you can have, in the same dist list, 1 burst value repeated with 2 different email addresses. but that's probably not the best solution.
so its best to have 2 caster jobs.
1 burst to a burst list
and 1 notburst to a single person or set of persons.
imho.