Born in a surveyor's tent pitched under a gum tree in Franklin Street, Adelaide, in the very early days of the colony, Bagshaw was educated in Jolly's School and Pulteney Street School. He showed early talent in mechanical matters and trained as an apprentice at his father's agricultural and viticultural engineering business, which he later headed. A significant figure in Adelaide society, he was a deacon of the Glenelg Congregational Church and a Justice of the Peace, and among other things served as a Councillor and then Chairman of the Mitcham District Council, and later a Councillor and Mayor of the Brighton Municipality.
His only published writing is an autobiographical account of a journey to the goldfields at the time of the gold rushes.