Bradley, who has also played for the likes of Heerenveen, Borussia Monchengladbach and Aston Villa, admits he is still learning to live with the burden that comes with playing in a city like Rome but suggests it is a challenge he fully accepts.
"I did an interview the other day and said that when you come to play for a big club, you learn what you can only learn at a big club. The reality is that until you're with a club like this, there's no way to experience these things," he said in an interview with the New York Times.
"The idea of stepping on the field every weekend with the pressure to win regardless of who you're playing, home or away.
"The pressure is always there. You look at how special a city this is in the context of the world and realize how much focus and attention is on us every time we step on the field. There's real competition for places on the field, two or three players for every role. You can train at your best every day, but even then decisions go against you. You have to be ready whenever your time comes.
"Maybe it's in the second half or as a starter a few days later in the next game. You have to learn to deal with the fact that a big team has a lot of players. There's no way to explain this. To understand you have to be here and live it every day."