Ross replied: "Are you sure you're the right person to be criticising others on the topic of mental health??"
A spokesman for Bridges said he had no comment to add.
Ross told the Herald he wanted to use his voice as an MP to raise important issues, including mental health.
"Sometimes that will involve calling out hypocrisy," Ross said.
"The Government Simon and I were part of let the [mental health] sector down and let the system reach crisis point. We now owe it to patients and mental health workers to work with the Government constructively.
"I'm happy to work with the Minister and other MPs on any issues in this area."
National spent the last few months of last year dealing with Ross, who quit the caucus - and was also expelled from caucus - released recorded conversations that embarrassed Bridges, and laid a police complaint over election donations.
In a statement last month, Ross said the apex of the saga was a "life and death" mental health crisis.
He sought the help of a psychiatrist, but was sectioned to the mental health unit at Middlemore Hospital after he tried to harm himself.
He said in his statement it wasn't fair on Bridges or Bennett to expect them to help with his mental health issues.
Bridges and Bennett have always maintained that their actions towards Ross were consistent with medical advice.
Ross is expected to return to Parliament when it resumes next week, and he has promised to serve the people of Botany and be an advocate for mental health services.
His office is in a different building to the offices of National MPs, and he will not have access to the corridors where the National Party is based.
At the National Party caucus retreat in Hamilton this week, National MPs said Ross' name was not mentioned and the party was focusing on building policy in areas such as law and order, the economy, and the environment.
But the spectre of Ross remained as Invercargill MP Sarah Dowie faced media for the first time since police confirmed an investigation into a text message she allegedly sent to Ross that included the words "you deserve to die".
The text message raised questions over whether there was a breach of the Harmful Digital Communications Act, which made it illegal to urge someone to self-harm.
Ross had previously named Dowie as one of the women with whom he had an extra-marital relationship
Dowie did not comment on her affair with Ross, adding police had not contacted her about the text message.
"I am committed to the people of Invercargill, just as I always have [been]," Dowie said.
Bridges said the party backed Dowie, and Bennett said the ongoing Ross-related drama was not a distraction for the party - only for the media.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• 0800 543 354 (0800 LIFELINE) or free text 4357 (HELP) (available 24/7)
• https://www.lifeline.org.nz/services/suicide-crisis-helpline
• YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757 or TEXT 4202
