Third seed Bencic is among the favourites to win the inaugural WTA International hard-court event in China and she started with a 7-5 6-2 victory over home-favourite Zhu Lin on Monday.
However, it was not all plain sailing for the Swiss, who surrendered serve on three occasions and double-faulted seven times.
Bencic, though, had too much quality for an opponent ranked some 109 spots below her in the world rankings and she now faces compatriot Romina Oprandi in round two following her 6-0 6-0 rout of Ho Ching Wu.
Riske, seeded sixth, also had some trouble with her serve in a 6-2 7-5 success over Cagla Buyukakcay.
She landed just 50 per cent of her first serves and was broken on three occasions, but eventually managed to show her superiority to progress in just over 90 minutes.
Olga Govortsova stands in her way of a place in the quarter-finals thanks to her 7-5 6-4 victory against 2010 French Open victor Francesca Schiavone.
Elsewhere, there were straight-set wins for Sorana Cirstea, Duan Ying-Ying and wildcard Liu Fangzhou.