Bobridge, Olympic champion Kim Brennan and rower Alexander Belonogoff feature on a third list released by the hackers who stole the medical records from WADA's data storage system relating to Therapeutic Use Exemptions (TUEs) granted to athletes.
The three-time world champion and Olympic pursuit silver medallist Bobridge, who was diagnosed with rheumatoid arthritis in 2010, was prescribed with prednisolone and glucocorticoids over a five-year period.
Bobridge said on Twitter that the exemptions were legitimate and were designed to treat his rheumatoid arthritis.
“Regarding the WADA hacks and "leaks"of my personal information I'd like to make it clear I have no problem with this info becoming public," he said.
“It is widely known that I have rheumatoid arthritis that, at times has left me barely able to grip the handlebars.
“I have taken appropriate medication for this terrible disease according to the UCI rules with their written permission.
The Australians were three of 11 athletes named on Friday along with British track star Laura Trott and double Olympic boxing champion Nicola Adams.
The Australian Sports Anti-Doping Authority (ASADA) didn't take long to respond to the release of the medical records, making it clear "such exemptions do not constitute doping."
"Despite the efforts of the hackers to twist these exemptions to prove foul play, in obtaining a TUE the athletes have operated entirely within the rules of clean, fair sport," read ASADA's statement.
"TUEs exist so that athletes who suffer from legitimate medical conditions can seek treatment.
"In the case of the three Australian TUEs leaked today, the athletes were approved to use medication to treat serious medical conditions, including allergic reactions and rheumatoid arthritis.
"Such exemptions do not constitute doping."
Earlier this week US gymnastics superstar Simone Biles, and Serena and Venus Williams had their TUEs leaked online along with cycling champions Chris Froome and Sir Bradley Wiggins.
The International Olympic Committee called the leaks an "outrageous" breach of confidentiality and have offered to assist WADA in communicating with Russian authorities over the matter.
Russian President Vladimir Putin, whose nation's track and field athletes were banned from competing in Rio, along with their Paralympians, claimed the records raise a lot of questions.
"It seems as if healthy athletes are taking drugs legally that are prohibited for others, and people who are clearly suffering from serious illnesses, major disabilities, are suspected of taking some kind of substances and banned from the Paralympic Games," Putin told Russian news agency TASS.