On reading the article, the term 'last May' in the Newspaper report of the Bigamy charge in which legal wife Annie is a witness, refers to the same year as the trial, 1905.
Annie's statement made on 21 July 1905, was that he told her he had a job in a mine and left her on 20th May to go to the job - it doesn't read that he left her, as in desert her. He sent her 3 sums of money while he was away and in fact, she tried to withdraw the warrant on him for desertion of the children, but was unable to. Annie discovered about a week before the trial, that he had married a young woman under an assumed name and was living with her in lodgings in Fitzroy, and he was then arrested on the 13th July.
http://nla.gov.au/nla.news-article9903848If your AGW is the same man with whom the young Miss HAYNES was involved, it appears to have been a short lived relationship - and perhaps 'in the nature of marriage' only and conducted a year before he got caught out with Isabella. That is, he had a mistress in Grace, - just like Isabella was, but perhaps didn't marry Grace and obviously, his wife didn't catch him (or at least didn't report it).
Intriguing, that the 1905 Newspaper article, it reports that AGW said there was "a great deal behind this case, as that woman (pointing at his wife) will find out later on"
South Australia, Australia, Police Gazette on 4th and 11 May 1904Information requested on Grace Beatrice HAYNES
Age 18½, Native of Victoria
Occupation Boot Finisher
Left her home in Northcote, Victoria on 21 March 1904 and went to Adelaide.
Was living there with a man named WALKENDEN as his wife, in furnished apartments in Kensington.
Left there on 27th April 1904.
5'3", Fair hair, fair complexion, dark blue eyes.
Her mother was in Adelaide looking for her.
Cheers
AMBLY