The 34-year-old, whose stay at the Memorial Stadium is the 15th loan spell of his career, was brought to the club by former manager Mark McGhee, who was sacked after Saturday's 4-1 defeat to York.
Ward was appointed as his replacement on Monday and inherits a club second-bottom in League Two.
Branston is predicting a difficult task for the new boss, but wants to be part of it.
"It's going to be a tough job for the new manager to come in and get us going," he told Press Association Sport. "But with the experience that he has got I am pretty sure he will steer the ship right.
"I will work hard for John Ward and hopefully he will see that, if he sends me on the way because I am an easy target then at least I will have worked hard.
"It's up to John to decide whether he wants me. First things first he has to come in and make an assessment, football is all about opinions.
"I want managers to think of me as a hard worker and grafter and I don't want them to think anything else of me."
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