The 28-year-old has spent the last few weeks away from the Premier League side's training ground following a message on the photo-sharing website, which appeared to make fun of the club's opening-day defeat.
| DEADLINE DAY ROUND-UP
|2/1||Sunderland are 2/1 with BetVictor to be relegated this season
The Scotland international also incurred the wrath of manager Paolo Di Canio after being photographed in a casino in the early hours of the morning at the back end of last season.
Bardsley was not given a squad number at the start of the current campaign, and saw a potential exit from the club hampered by a broken foot, but he could now be in line for a recall once recovered, after apologising for his actions.
"I would like to apologise to the club and supporters for my comments made on social media," he said in a statement.
"I understand how they may have been interpreted, and it was a serious error of judgement.
"I accept the punishment that has been handed to me by the football club, and will now focus my attention and efforts on rehabilitation and regaining my fitness."