There are 2 parts to the neck - رقبة which is the back of the neck, and the حلقوم which is the front.
Wiping the front is bid'ah - the Prophet (Saw) never did this
Wiping the back WAS done by the Prophet (Saw), and the regularity is what is disputed.
Those ulema who say the Prophet (Saw) did it reguarly, call it Sunnah (an act worthy of reward.).
Those ulema who say the Prophet (Saw) did it occasionally, call it mustahabb or adab. (a good thing to do)
Those ulema who say it is not established from strong hadiths call it mubah (allowed).
NOBODY i know of calls wiping the back of the neck a bidah.
Al kasani - the author of the Hanafi fiqh book Badaius sanaai, (died 587hijri) says:
الْفَرْقُ بَيْنَ السُّنَّةِ، وَالْأَدَبِ أَنَّ السُّنَّةَ مَا، وَاظَبَ عَلَيْهِ رَسُولُ اللَّهِ - صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ - وَلَمْ يَتْرُكْهُ إلَّا مَرَّةً، أَوْ مَرَّتَيْنِ لِمَعْنًى مِنْ الْمَعَانِي،، وَالْأَدَبُ مَا فَعَلَهُ مَرَّةً، أَوْ مَرَّتَيْنِ، وَلَمْ يُوَاظِبْ عَلَيْهِ
the difference between a sunnah and an adab (which includes mustahabb and mubah) is that the actions the Prophet (Saw) did regualrly, and left out only once or twice due to a particular reason, are called SUNNAH. As for an ADAB, this is what the Prophet (Saw) did maybe once or twice, and didnt keep on regularly doing it.