Is wearing a marriage ring "Bidah"?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Engagement/wedding ring is a small circular piece of metal, especially gold or silver, that is worn on the finger. If such a ring is of gold, then it is Haram for men as mentioned by the Prophet (Sallallahu Alaihi wa Sallam) when he took silk by his right hand and gold by left and said: "These two (items) are Haram for males of my Ummah and Halal for its females". Ahmad, Abu Dawood, Ibn Majah and al-Nasaai with a good chain of narrators. As for women, they are allowed to wear gold.
As for the engagement/wedding ring in your question, there is no evidence in Islam that legalizes such a thing. So, it is better, both for males and females, to avoid wearing the ring on the occasion of engagement or marriage, since this will constitute a form of imitation of non-Muslims. In addition, this habit arose among non-Muslims and we - Muslims - are ordered to avoid copying their habits, morals or…
The above-mentioned rulings apply only to engagement/wedding ring. Generally speaking, a woman can wear a ring of gold or silver and a man can only wear a ring of silver.
Allah knows best.