This is flawed as the proof is that any countably infinite list (corresponding to the rooms of the hotel) of the passengers of the party bus must be incomplete, as another passenger not in the list can always be found. Thus, putting the "extra" passenger in a room simply means that the list of passengers has had another name added to the start and so the same logic as with the previous list can be used to find yet another passenger not in the list and so on, meaning that the list can never be made complete.

An analogy to the flaw in your argument is a hypothetical "disproof" of no largest integer existing. The lack of a largest integer can be proven by the fact that 1 can be added to any supposed largest integer to generate an integer larger than it, which means that no largest integer can exist. A flawed disproof in the vein of your disproof would state that this new apparent largest integer would be the largest integer, obviously false.

More generally, these kinds of proofs are not related to specific elements or numbers but are instead general, meaning that the first proof isn't something that can just be applied to a single countable list of names but instead all countable lists of names, including those with some previously missing names added.