Bardsley was told to find another club by previous Sunderland coach Paolo Di Canio earlier this summer, but is back in the first-team fold under Poyet's regime and capped that return with the winning goal against Manchester City last weekend.
Following his decisive strike in the 1-0 win, Bardsley has declared that he would like to stay at Sunderland beyond his current deal, which expires at the end of the campaign.
He told The Mirror: "There were a few situations I was involved in which were difficult for me and my family at the time. As I say that's all in the past now, you've got to be mentally strong in this game or it will destroy you.
"I thought at the time my Sunderland career was over but the manager has given me a new lease of life and here we are talking about a 1-0 win over Manchester City. It's mad.
"I'd love to stay here but it's up to the club. I'm in the last eight months of my contract and I've got to perform. I love playing here and I'm just happy with what's happened since."
The 28-year-old has made more than 150 Premier League appearances for Sunderland since signing from Manchester United in 2008.