The Dutch goalkeeper may have kicked off the current campaign as Zeman's first choice, starting the first nine games of the season before suffering injury, but he has since failed to recover his place from Mauro Goicoechea, who joined Roma in August.
Stekelenburg even went as far as to question the need for a third keeper in the capital city, pointing to the presence of experienced Romanian stopper Bogdan Lobont in the squad.
Quoted in La Repubblica, he told Dutch magazine Sport Promotion: "I have ended up on the bench and Zeman has given me no explanation.
"I thought signing Goicoechea was unnecessary because Lobont and I were already here - two good goalkeepers.
"I'm targeting the World Cup and I'm tired of not playing."
The 30-year-old would subsequently apologise to his manager and his team-mate before training on Friday, with Goicoechea accepting what his colleague had to say.
"I have a great relationship with Stek," he said. "We had a chat and he explained to me that his words had been badly interpreted."
Three defeats from five games have seen Roma slip into seventh place and victory at Bologna will come without the contribution of Mattia Destro.
The 21-year-old striker will miss up to two months of action after injuring his knee against Inter Milan in the Coppa Italia in midweek.
Alessio Romagnoli, Daniele De Rossi and Marquinhos are also injured, with midfielder Erik Lamela suspended, while Henry Gimenez, Cesare Natali and Robert Acquafresca miss out for Bologna.
Michele Pazienza and Nicolo Cherubin are banned but Rossoblu boss Stefano Pioli is trying to stay positive despite recent setbacks.
Following a 2-1 loss at AC Milan, Pioli said: "Regardless of the defeat I think this has been a positive week.
"The team has improved and continues to improve. The league is difficult but I am convinced we will be ready when the next matches come round."
Alberto Gilardino's brace proved decisive in a surprise 3-2 win in Rome back in September, but Bologna have to think back to 2004 to remember the last time they beat Roma at the Renato Dall'Ara.