The former Miami Dolphins player agreed a four-year contract with the NFC North side earlier this week.
The 28-year-old told reporters: "When we were watching film and you see those safeties deep and safeties rolling over, double-coveraging [Lions wide receiver] Calvin Johnson. It's a running back's dream.
"We have to be able to run the ball in that situation. That's one of the reasons why I wanted to come here, to be able to bring a balanced attack and help take some of the pressure off Calvin Johnson and [quarterback] Matthew Stafford and just complement them.
"It just made sense. If felt right from the beginning. They really didn't have to sell me too much. They could have just pulled up one clip and I was already sold."
Bush was just short of the 1,000-yard mark for the Dolphins last season, scoring six touchdowns.