Bardsley will go down as one of the greatest goalkeepers in the women's game having won the Women's Super League, Continental Cup and FA Cup in a glittering career. She has also earned 82 caps for England and played a key role for the Lionesses at several major tournaments.
Having played no pre-season friendlies due to the number of players competing at the Olympics, City were then hit with a raft of injuries during the first half of the campaign, meaning they sat in mid-table at Christmas.
But with pressure mounting on manager Gareth Taylor, City have managed to turn things around since the start of the year by winning the Continental Cup and pipping arch-rivals Manchester United to third place to earn a spot in next season's Champions League.
Given all the issues City have faced, White is proud of the team's achievements this season, and in particular Bardsley's.
Speaking exclusively to talkSPORT, White said: "The group collectively have so much love and respect for Karen for what she's achieved in the game, what she's done for this club and what a servant she's been for women's football.
"Yes, it would be a lovely way to end her City career and football career. But for us, we want to keep that momentum going and send her off in an amazing way.
"But she knows how much this team loves her and how much we support her. We couldn't have asked for a better legend in women's football really.
"I think based on when we started the season, we would have taken your hand off really if we would have known that we would have secured a Champions League spot, won the Conti Cup and be in an FA Cup Final.
"Obviously, if we'd started differently, maybe we would have wanted something different. Yes, we wanted to win the WSL, but I think it just shows the character of this group.
"Inside the four walls of our training ground and collectively, the belief never wavered and we stuck together and we knew that we would be able to turn it around.
"We've shown that and we've shown great character, great desire and great belief in this squad. I'm really proud of the group."
City and Chelsea are hardly strangers having regularly battled for the WSL title in previous seasons, but it was Taylor's side who came out on top in the Continental Cup final in February thanks to goals from White and Caroline Weir.
Chelsea, though, have since made history by winning their third WSL title in a row under Emma Hayes, and have one of the best players in the world on their books in striker Sam Kerr.
"Her [Kerr's] goalscoring record and what she's achieved with Australia speaks for itself really and what's she's achieved in a short space of time with Chelsea," White says.
"She's a phenomenal talent and an unbelievable goalscorer [with] her movement and the different type of goals she has scored. For us, it's about watching her movement and trying to reduce the opportunities she has in front of goal.
"She gets those opportunities because other people create them. Their whole squad and their whole group are very talented. They didn't win the WSL by luck really. So, for us, it's about looking at all the individuals and the whole squad really."
White famously became England Women's top scorer after netting a hat-trick against Latvia in November and is now just three goals away from equalling Wayne Rooney all-time goalscoring record.
She has cemented her status as one of the most instinctive finishers in the women's game and as a West Ham fan growing up, cites Paolo Di Canio, Gary Lineker and USA forward Mia Hamm as key influences when she was younger.
The 33-year-old will be key to England's chances of success at this summer's European Championships on home turf and says the Lionesses are lucky to have head coach Sarina Wiegman.
She explained: "She's been great for us. She came in and she's a real leader. She's very detailed in what she wants from the team, but she's really supportive and wants the team to grow and develop and that's what's happened to the team since she came in.
"Each game and each camp, we've worked on something different and wanted to develop a different part of the philosophy which we want to showcase. It's basically for us to peak come the Euros. She's a really great coach and really supportive. We're really lucky to have her, to be honest.
"It's incredible that all the group games for England are completely sold out which is phenomenal and it shows that people really want to come and watch women's football and support the game.
"It would be amazing if selected, [as] the squad hasn't obviously been announced yet. I'm trying everything to be selected for England.
"I think when we've had the squad together, we want to really make the country proud and our family and friends proud and the whole country to get behind us and support us and feel that real buzz that the men had, which would be an incredible feeling."