The 25-year-old pushed for a move down south to be closer with family prior to Bruce being appointed as Benitez's replacement.
"It was a big reason why in the summer I wanted to stay," Hayden told Clinton Morrison in an interview for BBC 5 Live Sport.
"I had Rafa Benitez for three years and he brought me to the club and put a lot of faith in me so for a manager to come in after him, obviously, there was a lot of uncertainty around my future.
"For a particular manager to come in, I couldn't have wished for a better one because I worked with him [Bruce] when I was at Hull. I went on loan to Hull when I was younger for a year and he was the manager there and he took me under his wing when he was there, helped me a lot and helped improve my game.
"So for him to come back in and be the manager was big for me."
On Bruce's personality, Hayden added: "It's just the personal side of it. I wouldn't say he's a cold manager.
"You feel you can knock on his door or you can speak to him about anything. It could be about anything in general, life, cars. Whatever you're chatting about, he always gets involved in the banter or gets involved in the conversation.
"He's got some great stories from the past of his experiences that are always good to listen to. He's just a bubbly character, really. He's never really too down or sulking or not speaking.
"He's always there at training - that's another big thing - and he never misses a day of training. Even when it's subs day or when you're on the bench and you've got the next day at training, he's still out there.
"Since he's come in, I don't think he's missed a day of training. Even if he's been a bit under the weather or whatever it is, he's always been there so I think that's a massive bit as well because these days, some managers sit in their office or they don't come out to training every day or they let their assistant do it whereas he's always there watching, having banter.
"I think it's just the personal side of it. I think that's the most important thing with him. He's just a nice guy."
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