The lady took to social media to thank Bob and another customer for saving her on "the day where everything went wrong".
Despite it pouring down with rain, they found some jump leads and managed to start the car after its battery had gone flat.
The customer, who says the world needs more people like Bob, posted on Facebook to say: “The battery had died and as things couldn’t get worse, it started to absolutely chuck it down with heavy rain and I couldn’t get the electric windows to go up.
“My baby was getting drenched and was screaming ... I was getting drenched and was panicking. Enough was enough for me and I burst into tears.”
Another customer saw her distressed state and, with the help of Bob, they got some jump leads and managed to get the car started. The customer, who had been to the Asda pharmacy, said: “I really had the day from hell and these guys saved me. We really need more people like you about and the world would be a much happier place.”
Bob, who's worked at the store for five years, said: "I noticed there was a customer looking quite stressful on the car park, so went over to see what the problem was. She had an issue with her car not starting and had a young child with her that was crying that wasn't very well.
"There was already another member of the public there and between us we were able to get some jump leads and managed to get the customer's vehicle started. I could see how upset the customer was and kept talking to them to hopefully keep her calm.
"She was extremely grateful and kept thanking me but I just told her that is what I am here to do. I am just glad we were on hand to get her on her way and get her poorly child back home safely."
The mum, who asked not to be named, says she wanted to share what had happened to show her appreciation for what Bob and the customer had done for her.
She told the Manchester Evening News: “Thank you so much for what seemed to you like a little helping hand but to me was a bloody lifesaver."
Store manager Lee Buckley says his actions were typical of Bob's kind nature and that everyone at the store is proud of him.
He said: "Bob is such a kind and passionate colleague who is always on hand to help out any customers who need support.
"He is a much-loved member of the team and is often being recognised by our customers for his friendly attitude and dedication to his role.
"I am so proud of him for how he has gone above and beyond to help one of our customers. He is such a humble person that he feels overwhelmed with the kind recognition this has brought on social media and in typical Bob fashion just saw it as 'what he does' as part of his responsibility as an Asda colleague. Everyone here at Asda Stockport is extremely grateful we have a colleague like Bob who does an outstanding job day in day out and is there for our customers when needed."