How to find a bigamist
Many bigamists were found out and tried in a court of law. Trials were usually reported in newspapers, so looking at these is a good place to start. If your ancestors were from the UK, the British Newspaper Archive (mentioned above) is the best available collection. For more on the BNA, see this post. Access to this collection is also available with some Findmypast subscriptions.
For information on free newspaper collections in some countries see: Where to find Free Online Historical Newspapers.
There were bigamy trials at the Central Criminal Court in London (known as the Old Bailey). The wonderful free resource, Old Bailey Online, has access to proceedings between 1674 and 1913.
You can also find Court and Legal records on the main database sites like Findmypast and Ancestry.
If a suspected bigamist in your tree was not caught, then of course there’ll be no newspaper records. So, in these cases it will be very difficult to prove bigamy, unless you have DNA evidence.
If you find someone living with another family who you suspect may be your relative, have a good look at him. Get his marriage record and look for clues. Who were his parents and who was the witness? Are these names familiar? Can you find his birth record or is he on earlier census records? Try and rule him out.
You may also be interested in: How to Deal with Illegitimate Ancestors
Also, check out these useful books: