"I'm not going to hide the fact that I put my name forward for the job," said Bridges, who is unsure of the Jets plans after they were taken over by Chinese company Ledman Group in June.
"Whether I have the experience or haven't, I'll back myself all the way.
"Then an opportunity came up to join Teddy as a package. It would be silly not to want to work under somebody with his experience and pedigree.
"The Premier League is massive in China, and having two ex-Premier League players might appeal to the Ledman Group, or it might not."
Bridges added: "[Sheringham] has been a gaffer over there (in England) and has worked under the best manager in the world in Alex Ferguson.
"There is no doubt that you learn a lot from guys like that. I have spoken to some of the boys at Stevenage. They say he has a good tactical mind and his management is superb.
"His door is always open and he tries to let the lads play with a smile on his face. You can be a tactical genius, but if you haven't got the dressing room behind you, then the team won't perform."
Scott Miller and his assistant Luciano Trani were sacked by Newcastle last week.