Bardet, who finished third behind Froome at the Tour de France in July, said that the news that the Team Sky rider had twice the permitted level of asthma drug salbutamol in his urine after stage 18 of the Vuelta a España had an impact on everyone in the sport.
"This is not good news for cycling. Pretty much everyone gets hit by something like this, cycling's credibility first and foremost," Bardet told AFP.
"We really could have done without it. It's not something anyone can rejoice about. Let's hope that a swift and objective probe can clarify the facts and leave no doubts about what happened."
As the World Anti-Doping classifies salbutamol as a specified substance, Froome has not been given a provisional suspension. However in line with the UCI's anti-doping procedure, Froome's case will now be referred to the Legal Anti-Doping Services (LADS), with the rider and Team Sky being required to explain the elevated levels of salbutamol in Froome's system.
Riders have previously received sanctions for delivering high levels of salbutamol, with Diego Ulissi receiving a nine-month ban in 2014, and Alessandro Petacchi being banned for a year in 2007. However other riders have been cleared for medical reasons.
In a statement issued as news of Froome's AAF emerged on Wednesday, Team Sky said that it would be looking at a range of factors to explain the high levels of salbutamol in Froome's urine, with the aim of having its rider cleared through a pharmacokinetic study.
"There is considerable evidence to show that there are significant and unpredictable variations in the way salbutamol is metabolised and excreted.
"As a result, the use of permissible dosages of salbutamol can sometimes result in elevated urinary concentrations, which require explanation. A wide range of factors can affect the concentrations, including the interaction of salbutamol with food or other medications, dehydration and the timing of salbutamol usage before the test."
Froome himself has also denied any wrongdoing, saying that he will comply fully with the UCI's investigation.
"It is well known that I have asthma and I know exactly what the rules are. I use an inhaler to manage my symptoms (always within the permissible limits) and I know for sure that I will be tested every day I wear the race leader’s jersey," the 32-year-old said.
"My asthma got worse at the Vuelta so I followed the team doctor’s advice to increase my salbutamol dosage. As always, I took the greatest care to ensure that I did not use more than the permissible dose.
"I take my leadership position in my sport very seriously. The UCI is absolutely right to examine test results and, together with the team, I will provide whatever information it requires."
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