Rooney had stated his desire to leave Manchester United before performing a dramatic U-turn on Friday and signing a new five-year contract with the club.
The deal makes him the highest-paid player in United's history on around £150,000 per week, and Bruce admits the finance present in football combined with players' sense of self-worth is "a cocktail for disaster".
"The hardest part of managing in the Premier League is dealing with egos," he said.
"It's the man-management, the advice and looking after players. The one thing you don't want is your football club ending up on the front pages repeatedly.
"The difference between my time playing and now is the player power that's come since the Bosman ruling. You are dealing with young footballers who have become millionaires at a very young age and it can be difficult to handle. When even a club of Manchester United's stature are struggling with it, it shows how difficult it is.
"All you can do is try and gain their respect. Sometimes that's difficult. The vast majority of players are of a similar ilk and background, and I don't mean that disrespectfully.
"Then you add to that the power that money gives. It's a cocktail for disaster. You just have to hope the player gets good advice."