According to a recent article in Aeon, she traveled from Amsterdam to Paris in 1915 and back to Amsterdam in 1916 - apparently by legal means.
How did travel between countries on opposite sides of the front line work? Both in terms of route and in terms of bureaucracy, what were the restrictions and available routes?
Travel in this period was still possible - if risky - by sea, if one was travelling to or from a neutral port such as Amsterdam, and doing so under a neutral flag. In the case of Mata Hari, she travelled to and from Amsterdam via Spain and Portugal.
Her fatal error was to travel, in the autumn of 1915, on a ship that called at Folkestone, on the British coast, where questioning aroused the suspicions of a British intelligence agent named Captain Dillon. She was put under surveillance, and eventually arrested and tried as a German agent by France.
Source
Pat Shipman, Femme Fatale: Loves, Lies and the Unknown Life of Mata Hari