Goalkeeper Adam joined the club from Hungarian side Vasas Budapest, and spent time out on loan at Crewe Alexandra in 2009. He made his debut for the club in 2010, keeping a clean sheet in a 1-0 home win against Southampton in the League Cup. His league debut would come replacing Jussi Jaaskelainen after he was sent off against Birmingham City. He kept his place until the Finnish keeper returned following his suspension.
In 2011/12 Bogdan would become first choice, and was the supporters Player of the Year the following season following a string of good performances including a saved penalty at Old Trafford. However his performances could not stop the club from suffering relegation at the end of the season.
He signed a contract extension in November 2012, prolonging his stay at the club til the summer of 2015. He would be the first choice goalkeeper again as the club failed to win promotion back into the Premier League, making way for Andy Lonergan in cup games.