I plan on telling the man sitting next to me on the bus to leave.
Can you explain why you want him to go away?
His breathing is disturbing me and I just want to read.
While it's okay to tell someone that they are making you feel uncomfortable, it isn't appropriate to do so when it is something that they can't control like the way that they breathe. It's inappropriate and rude to ask the man to leave the bus since he isn't intentionally trying to disturb you. You should understand that the man has the same right to use public transit as you do and you need to share the space equally.
I would never get into a fight with anyone over being on the bus, but my sanity is more important here.
You need to be more accepting of others when you are using public facilities and sharing spaces. The man can't control his breathing and you should be mature and control your emotions. If it's truly distracting then you can always read when you get home.