Here's what went down ... the "It's My Life" singer was filming a music video for his song "People's House" on the John Seigenthaler Pedestrian Bridge in Music City around 6 PM, when JBJ noticed a woman in need of help.

Check out the video ... the woman in question appeared to be gearing up to jump off the famed bridge -- but Bon Jovi then approached her and spoke to her, convincing her not to end her life.

Sources with direct knowledge tell TMZ ... Bon Jovi routinely deals with people in crisis from hunger to homelessness, among other issues, through his work with his foundation, the JBJ SOUL FOUNDATION. He has extensive training in speaking with individuals experiencing a crisis ... but he did what anyone would have done in that situation.

Bon Jovi even helped pull the woman over the side of the railing, with assistance from another bystander ... who also appeared to be talking to the woman.

The Nashville Fire Department and the Metro Nashville Police Department both responded to the scene ... with Nashville PD Chief John Drake applauding the singer for taking swift action.

He added ... "It takes all of us to help keep each other safe."

It's unclear what exactly the singer said to the woman ... but Bon Jovi is known for singing an inspiring song or 2.

Take his band's 1986 mega anthem, "Livin' on a Prayer," in which JBJ sings about powering through hard times and being there for loved ones.

Cleary, Bon Jovi was at the right place at the right time ... and can now add "hero" to his already impressive résumé.

We've reached out to Bon Jovi's team for comment ... so far, no word back.