Bid'ah actually means inventing some new things in religion, and claim that it's from religion. Like praying the morning prayer six raka't. As AMuslimDude213 said, sending salam on the Prophet (Peace be upon him) isn't an invention in religion because God already told us to make Salah on our beloved prohet (Peace be upon him). Praising the prophet is one of the best things as the Prophet himself (Peace be upon him) said "None of you will believe until I am more beloved to him than his children, his father and all people.”, and he also said “There are three things that if someone were to seek refuge in them they would experience the sweetness of belief. They are that Allah and His Messenger are more beloved to him than anything else; that he loves a person only for the sake of Allah, and he loathes the notion of reverting to disbelief as much as he would loathe to be cast into the Fire.”
