He told PRWeek he wanted to see more media access to senior officers and savings made, particularly on the council's publication Bedford News, which he may consider scrapping altogether.
He is also considering merging the PR team into a newly created information and research centre, which would be more 'open to ordinary individuals and members,' he said.
In a campaign leaflet to residents Branston says: 'Senior officers should be available to answer questions from the media instead of hiding behind the PR department.'
He told PRWeek that his criticisms were not referring to PR staff but to council-wide attitudes to PR. 'It's not their (PR staff) fault,' he said.
Council publicity and corporate communications officer Debra Munford works alongside two temporary comms staff.
She said the Bedford News was cheaper to produce than many similar publications by other councils but would not reveal its cost. Branston estimates it costs more than £100,000 per year to produce.
In relation to Branston's comments on the handling of media enquiries she said the council was always prompt with answers.
'But those answers are not always necessarily what they want to hear,' she added.
Branston has confirmed he will step down as chairman of the Bedfordshire publishing group if elected.
One of the group's papers Bedfordshire on Sunday is still involved in legal proceedings with the council.
Three council officers, including CEO Shaun Field, sued the paper and local Conservative agent Stewart Lister (now a member of Branston's campaign team) over stories concerning the borough elections of May 2000.
The paper is appealing against a decision earlier this year, in this case in favour of Field, who also lost part of his claims.
Both the other officers lost their claims.
Branston was this week made 9-4 favourite by Bedford-based Chapman Bookmakers to win the election on 17 October.