Ms Bradbury, 43, infuriated Ms O'Reilly, 57, after suggesting in a newspaper interview that her former fellow Countryfile star was not a victim of ageism.
Ms O'Reilly won an age discrimination case against the BBC in 2011 over the decision to drop her from the rural affairs show.
Former Watchdog host Ms Bradbury and Matt Baker were among new presenters who joined the revamped programme while John Craven was kept on.
When Ms Bradbury suggested the older presenter's departure was to do with changes to the show's format, Ms O'Reilly accused Ms Bradbury of "a***-licking" and advised her to "look at the legal case (because) one day you might need it".
The row began after Ms Bradbury, asked whether she was uncomfortable with her Countryfile role following the furore over Ms O'Reilly, told a newspaper: "I've been through millions of programme changes where they say 'Sorry, love, we've changed the slot.'"
Ms O'Reilly hit back, writing to Ms Bradbury on Twitter: "Before you make ill-informed statements I suggest you look at the legal case - one day you might need it.
"Until then good luck with the a***-licking."