Twenty-year-old Bhuvana, globally ranked a lowly 842 in singles, got past her left-handed British opponent - ranked 396 in the world - after rallying from the loss of the opening set to squeak through 1-6 7-5 6-4.
The Indian girl, who converted five out of 14 break point opportunities, will meet either eighth seed Xinyun Han of China or Belgian qualifier Britt Geukens in round two.
She had entered the main draw after getting past Lee Pei Chi of Chinese Taipei in the final qualifying round yesterday.
Rishika is to meet either Chinese second seed Kai-Lin Zhang or Rashmi Teltumbde, another home country wild card, in round two.