Bruce made his dugout bow for the Blades in 1998 before departing the following summer, but ahead of his team's FA Cup semi-final with the League One club, the Tigers chief has placed on record his gratitude for his former employers.
The 53-year-old is quoted by Sportinglife.com as saying: "I'll be eternally grateful to them because the one thing it did was give me a chance in management.
"It put me on a learning curve, very quickly. I think that I had six chief executives in one year and they were difficult times. That's an understatement."
The winner of Sunday's fixture will play either Arsenal or Wigan Athletic in the final.