Ms Barr, 46, from Lancaster, was diagnosed with incurable abdominal cancer last year and died last month.
In 2019, she gave up her role presenting North West Tonight to retrain as a firefighter.
Colleagues from Lancashire Fire and Rescue Service (LFRS) and representatives of the Guide Association, for whom she was a volunteer, formed a guard of honour as her coffin was brought to Beetham Hall Crematorium in Milnthorpe.
Following her death last month, former BBC North West Tonight colleague Annabel Tiffin described her as "a feisty, fearless woman".
Presenter Roger Johnson said she was "courageous in so many ways" .
Former BBC Breakfast business presenter Steph McGovern posted on X she was "the life and soul of the BBC newsroom", and "funny, smart and fearless".
LFRS said it was "deeply saddened" by her death, adding: "Beccy was a dedicated and courageous firefighter who served with professionalism and compassion.
"She was an enthusiastic and warm person who became an inspiration to many."
Ms Barr started her journalism career at the Blackpool Citizen in her early 20s and then worked for Bloomberg News and CNBC in New York before moving back to Lancashire and joining the BBC.
She followed in her father's footsteps when she decided to become a firefighter, joining Red Watch in Blackburn.
She also studied for an MSc at Bournemouth University's Disaster Management Centre and will be posthumously awarded her masters with distinction.
She was a Girlguiding leader for many years, most recently running a Rainbow unit at St Paul's Church in Scotforth.
She also participated in IronmanUK and several long-distance athletic events.