It follows an announcement by neighbouring New Zealand -- whose flag is nearly identical to Australias -- that it will hold a referendum on the issue.
Both flags feature a miniature version of the Union Jack -- the national flag of former colonial power Britain -- in their top-left corner, along with an array of stars.
"Believe it or not, its not an issue that actually draws much attention in Australia," Bishop told BBC radio late Tuesday.
"I believe we will stick with the flag. Theres no great demand to change it and many Australians have fought and died under that flag, sadly.
"We have competed in Olympic Games under that flag and theres a sense of pride in it."
New Zealands Prime Minister John Key this week pledged to hold a referendum on changing his countrys flag if he wins a third term in office in September elections.
He personally favours a silver fern on a black background, a national emblem already used by New Zealands sporting teams.
The flag issue is raised periodically in Australia, along with the prospect of breaking ties with Britain and becoming a republic. Britains Queen Elizabeth II remains Australias head of state.
The queens former representative in Australia Quentin Bryce reignited the debate late last year when she expressed support for replacing the monarch with an Australian head of state.
Ahead of Australias elections last September, state broadcaster ABC asked more than 1.4 million people their views and found 38 percent were in favour of cutting ties to the British monarchy while 20 percent were neutral.
Asked whether Australia would "keep the flag" and "keep the queen", Bishop -- who is in Britain for annual talks between the nations foreign and defence ministers -- said: "For the time being, most certainly."