Seven candidates are vying to succeed Bach in an election in March, with the German stepping down in June 2025 after 12 years in charge.
Athletes from Russia and Belarus were allowed to compete under a neutral flag at the 2024 Paris Olympics, having met strict criteria.
However, momentum appears to be gathering pace for Russia to be readmitted under its own flag.
One of the favourites for the IOC job, Juan Antonio Samaranch Jr, told AFP in September that Russia remained in violation of the Olympic Charter, but said "once the reasons for the suspension are removed, we will have to work very hard to get Russia back".
Mr Bidnyi, though, said that over two years into a war sparked by Russia's invasion of Ukraine, there should be no softening of the line.
"Our position is clear - sports cannot be a propaganda tool for an aggressor state," he said.
"There can be no return under the national flag of a country that continues to wage the largest war in Europe since World War II.
"If IOC presidential candidates want to be global sports leaders, they must embody the principles of justice."
Mr Bidnyi, 45, who has been in his post since November 2023, said the candidates should come to Ukraine to see the devastating impact of the conflict.
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