What is the most polite way to tell someone that they have bad breath without being too offensive?

I would offer mint as well or suggest getting some water to drink. Making these suggestions or offering the mint to everyone will make it more subtle. If the other party declines those options, I would simply keep my distance (if they are just acquaintances). If said party is my close friend, I will just let him/her know that it's better to take the mint/buy some drinks. ;)