A lot of visitors find this blog after asking that question in Google. The following page provides links to features that tell the story of the different identities that have been adopted during the history of the club and its predecessor, Manningham FC:
About BCAFC colours, crests and nicknames – Wool City Rivals
The principal identities have been the civic boar and the bantams nickname and you can discover the origins of both. You can also discover the various monogram badges that have been used.
I occasionally get questions from people who have inherited or discovered old Bradford badges and I am happy to assist as best I can. You can contact me via this site or by Twitter DM to @jpdewhirst