However, what is the order when assigning the bonus point for being in the same room as the prince?
This is covered on p6 -- gain it in order of most popular to least.
As far as I can tell, there's not much reason not to follow the Prince around as much as you can. It depends on his route and how many Dances you want to play (which makes it harder to get information), but sharing a room is just as much an opportunity as a danger. Then again, there is probably some strategy about which people to follow, given their relative popularity and how much information you think they have.