Ganna Rizatdinova of the Ukraine is ranked first after two of four events in the all around standings after placing third in both ball and hoop for a score of 36.332 points.
Bezzoubenko placed 22nd in the ball event on Monday but dipped to 42nd in her hoop routine for a combined score of 32.582 and sits just outside the top 24 needed to qualify for the all around final.
Carmen Whelan of Toronto, competing at her first world championships, is ranked 43rd all around with 30.916 points.
Qualification for the all around final continues on Wednesday and Thursday with the clubs and ribbon events.
“Patricia has had some difficulty with her hoop routine this year but she also was very steady at the last World Cup before worlds,” said Canadian national team director Teresa Orr of Toronto.
“All her routines are more difficult this year than at the last world championships. If she’s consistent and does what she can do with her clubs and ribbon routines over the next two days, hopefully she’ll be in that top 24.”
Bezzoubenko qualified for the all around final for the first time last year and went on to finish 24th.
More is at stake this year with the world championships doubling as the first of two qualification meets for the 2016 Rio Olympics.
The top 15 all around in Stuttgart will qualify directly for the Games, while the next 23 highest ranked all around will advance to a final Olympic qualification meet in April.