I think that to get from Heathrow to Oxford a train may have been nicer (not entirely sure of the route but I expect you would need to go into central London then get on an over ground train). Buses are always subject to traffic and especially if going between cities there can be quite large delays.
If I were travelling from a London airport to Southampton (I live in the UK and we drove to Southampton) I would get a train or the Disney transport option.
I also found it odd that cereal via room service was already in a bowl, I was expecting boxes. I also expected to get cartons of milk not pre-poured.
We didn't see a direct train from the airport to Southampton and didn't want to switch trains with our luggage. We flew in and traveled to Southampton the day before the cruise so Disney transportation was not available. Is there a direct train?