The First Minister was accused of presiding over “a culture of secrecy and cover up” after refusing to say how many investigations had taken place and what their outcomes were.
It comes amid renewed questions over complaints allegedly made by civil servants against former SNP minister Fergus Ewing.
Allegations were reported to have been made by three officials against Mr Ewing, who is now a backbench MSP.
Ms Sturgeon previously refused to reveal the outcome of this probe, citing “GDPR privacy issues”.
Speaking during First Minister’s Questions, Scottish Labour leader Anas Sarwar asked how many investigations into bullying have taken place, if they had concluded and what the outcomes were.
Ms Sturgeon said: “I’m not in a position to get into these issues because there are very considerable legal data protection issues that I am bound by.
“Governments have a duty of transparency, but governments also have a duty to abide by the law on privacy and on data protection.
“A complaint by its nature includes personal data on both the complainer and the person complained about.
“This personal information can only be made available outwith the narrow confines of the complaint if there is a lawful basis within GDPR to do so.”
Mr Sarwar insisted he was not asking for confidential details, but the outcomes of investigations.
He added: “After the allegations against Alex Salmond, and then [former SNP minister] Derek Mackay, and bullying findings against UK Government ministers, we need to restore trust in politics.
“And that must start with complaints being handled transparently.”
Ms Sturgeon said she and the Scottish Government “take any complaints about any ministers very seriously”.
She added: “These are serious issues, they have to be treated seriously, but they also have to be treated within the confines of the law that applies.”
Mr Sarwar insisted the public deserve to know the outcomes of investigations.
Speaking after FMQs, he said the issue was indicative of “the culture of secrecy and cover ups at the heart of this government”.
He said: “The public deserve to know the outcome of this investigation as a matter of transparency.
“The fact that Nicola Sturgeon can’t escape from is that her government and the SNP operate in a culture of secrecy and cover up.”
Mr Sarwar also hit out at “a culture that has contempt for journalists, and anyone who dare ask a difficult question of this First Minister”.
He added: “After 15 years of being in government, why does Nicola Sturgeon think it’s one standard for her and another standard for everyone else.”
Responding to these claims during FMQs, Ms Sturgeon insisted: “I stand to be corrected, and somebody can challenge me on this, but I’ve probably answered more questions from journalists over the past couple of years than any other political leader anywhere on these islands.”
A spokesman for the First Minister later refused to say how many bullying complaints had been upheld.
Asked if the policy of the Scottish Government is that if a minister is found to be a bully, people will never know, he said: “I’ve got nothing to add to what the FM said.”