Seventh-ranked Bouchard, coming off a breakthrough season that saw her reach the final at Wimbledon and two other Grand Slam semifinals, was no match for the No. 16-ranked Safarova in the tournament opener at Perth.
Vancouver's Vasek Pospisil played Adam Pavlasek in the men's singles match to follow, with the teams also set to play a mixed doubles match.
Australia was scheduled to play Poland in the night session at Perth Arena.
On Monday, Serena Williams is scheduled to play her first match for the United States against Italy, while Andy Murray leads Britain against France.