Bradley's initial appointment was met with some scepticism and he is yet to win round all of his doubters.
The American recorded a first victory at the sixth attempt in the last round of fixtures as Swansea fought back to beat Crystal Palace.
Swansea are two points adrift of safety ahead of this weekend's assignment, a tough trip to Tottenham, but Bradley is confident results will improve.
The 58-year-old feels the only way to silence his critics is to ensure Swansea pick up points and pull clear of danger in the weeks ahead.
"I understand there are a few sceptics out there, but they have not seen how I work or paid much attention," he told the BBC. "I can only go about my work and let that speak for itself.
"The idea in life is to find new challenges, that's how you grow and get better.
"You want to prove yourself, but accepting challenges and being excited about testing yourself is a positive thing.
"Some will like me, some won't but the results will speak for themselves."