Davies joined Hull in the summer after the Tigers secured their return to the top flight, and has helped the KC Stadium outfit into the top half of the table after seven games of the 2013/14 season.
And the former Aston Villa and Birmingham stopper - who scored his first goal for his new team against Cardiff in September - told Soccer AM that City boss Bruce has been key in the club's ascent.
"The way Steve works with the squad is [great] and the demands he puts on us we are able to carry out," said Davies, who has also played for Luton, West Brom and on loan at Leicester.
"He hasn't tried to sign players and turn them into something, he has signed players knowing what their gifts are and hopefully our form can continue."
Hull sit one place and one point above reigning Premier League champions Manchester United in the standings, after winning three and drawing two of the matches so far.
And Davies, 28, says that if the Tigers end the season in a better position than David Moyes' men, he will celebrate in a very unique style.
"I said tongue-in-cheek that I would streak around the KC Stadium if we finished above Man United and I am still quite confident that won't happen," he explained.
"I think United will kick on as they are a good side, but if we do finish above them that, in my opinion, would mean a Champions League place so I would be happy to do it!"
Davies sported a cut on the Soccer AM sofa, which he sustained in Hull's previous game with Aston Villa after clashing heads with Czech striker Libor Kozak.
The London-born player has published images of his wound on the internet but says it will not stop him from getting stuck in on the pitch.
"I got a bit of stick for putting pictures on Twitter of my eye and someone said they thought I was trying to get a new contract for being brave," added Davies.
"I was lucky it was along the line of me eyebrow - I can't now style my eyebrow but that is Aaron Lennon's style and not mine, but I wasn't worried about it and will get on with it because I am a centre-half."