The only person(s) I have ever seen referred to as Bride(s) of Christ are nuns.
As to "the earliest days" the only religion whose earliest days I have ever taken a serious interest in is Paganism in all its multifarous variations.
JPG and Rhiannon are quite right. The original references to the Church as the Bride of Christ are in Ephesians 5 & Revelation 19:7. The influential and sexually confused Church Father, Origen, wrote numerous allegorical interpretations of the OT, and the Song of Solomon was given an extensive exegesis claiming that the book represented "the love which exists between Christ and his Church". It is highly unlikely whether this erotic poem was originally intended to have any religious significance at all - but then lots of things got into the OT without there being any apparent religious significance in them - the book of Esther for example.
Bach was particularly fond of giving musical settings to this idea, and his famous cantata "Sleepers Wake" is all about the arrival of the "Bridegroom" (Jesus) in the hearts of the faithful, nuns and otherwise.