The best way (and the only way I know of) to stop the nuisance of natural bosses is to stay underground for the entirety of the night.
If you happen to return above the underground or cavern layers, the boss is probaly going to show up.
This method will NOT stop a boss from killing you after it actually spawns.

TIPS

• Once the initial message appears saying something around the lines of "This is going to be a terrible night." (The Twins) or "The air is getting colder around you." (Skeletron Prime), it's best to get to a nearby cave system as fast as you can.

• Don't try to fight Mechanical bosses that spawn naturally just as you reach Hardmode unless you consider yourself to be extremely good at the game. Better to use this method. This should be pretty obvious, but it's safe to mention.

• If you aren't well-suited for enemies that spawn underground, it would be a good idea to barricade yourself in some way.

EXCEPTIONS
• This will not stop any events. Things like Goblin Armies or Pirate Invasions will still happen, even if enemies from them won't spawn underground (But you can wait out a Solar Eclipse underground).