On 3 November 2004 Louisa Herron Thomas published a most informative and helpful text on the Slate site in answer to the many enquiries about moving to Canada. Her piece was called "How To Move to Canada. Will they take us in?" The expression bush dodgers is used without quotes, showing that it is a fully accepted term.

In the following day's issue of The Martlet: The University of Victoria's Independent Newspaper, Megan Stewart wrote a profile of several Bush dodgers in an article entitled "Bush dodgers and political refugees". In writing about one of them Stewart linked the Bush dodgers of the present to the draft dodgers of the past. The paradigm is clear: the modern equivalent of draft dodgers is Bush dodgers.

slate.msn.com
Louisa Herron Thomas, "How To Move to Canada. Will they take us in?", 3 November 2004
    Bush dodgers arriving in Canada must also provide a valid passport, two copies of a detailed list of all personal items brought into the country and two copies of a list of all items on the way, and proof of enough funds to cover expenses for the first six months.

The Martlet: The University of Victoria's Independent Newspaper, 4 November 2004
Megan Stewart, "Bush dodgers and political refugees"
    Her parents dodged the draft in the ’60s and raised their family in Kelowna, B.C.