During the winter break, Bakaj announced his departure from Laçi along with the striker Julian Malo, and, in the first days of 2010, he joined Besa Kavajë on a free transfer for the second part of 2009–10.
Following recommendation from his cousin Elis Bakaj, Edvan was given a trial at newly promoted Liga II side Alro Slatina. At first it was believed to be an unsuccessful trial as he did not impress in a friendly. However, on 15 July 2011 he signed a contract at the club and joined his cousin and former team mate Elis in Romania.
On 8 August 2012, Bakaj signed a one-year deal with Laçi. He made his return debut with the club on 24 September 2012 during the league match away against Skënderbeu Korçë, where Bakaj conceled three times for a 3–0 defeat.
On 4 May 2014, Bakaj scored his first career goal during the 6–0 thrashing of Kastrioti Krujë, valid for the 22nd week of 2013–14 season, scoring from the penalty kick. He left the team after the end of the season by terminating his contract by mutual consensus.
On 25 July 2014, Bakaj signed a two-year contract with Tirana, taking the vacant number 31 for the 2014–15 season. He made his league debut with the club on 30 November 2014 against his former side Laçi, keeping his first clean-sheet of the season in a goalless draw at home.
During the 2014–15 season, he served mostly as a back-up for first goalkeeper Stivi Frashëri, but he took his place in early March 2015 after the match against Partizani Tirana, were Frashëri made a mistake that was decisive for the faith of the match. Bakaj ended the season with 16 appearances in all competitions, including 9 in league, with Tirana who finished it in the fourth place and was eliminated in semi-finals of 2014–15 Albanian Cup against Laçi with the 1–0 aggregate.
He left the club on 7 August 2015 after being told that he was not in the plans of the technical staff, but, five days later, however, a call from the club's president Refik Halili made him to change his mind and return in training. Bakaj was the starting goalkeeper of the team during 2015–16 season, making 29 league appearances, collecting 2610 minutes as Tirana finished in 5th position. He also played in 5 Albanian Cup matches, as Tirana was eliminated in the quarter-final to Flamurtari Vlorë.
During 2016–17 season, with the arrival of veteran Ilion Lika, Bakaj was dropped to second choice, making only 5 appearances, all of them in cup, as Tirana was relegated for the first time in history, and won the cup for a record 16th time. In August 2017, Bakaj terminated his contract by mutual consent due to lack of playing time.
On 10 August 2017, Bakaj completed a transfer to Liria of Football Superleague of Kosovo for an undislosed fee.
Bakaj has been a former youth international player of Albania, player three and two matches respectively with U17 and U19 side.
Edvan is the cousin of Elis Bakaj, an Albania international midfielder and player of His cousin Elis Bakaj is an Albania international midfielder who plays of Kukësi. They were teammates for two years at Tirana.As of 15 August 2015
Albanian Cup: 2009–10
Albanian Supercup: 2010
Albanian Cup: 2012–13
Albanian Cup: 2016–17