While college seniors often enter the MLS SuperDraft, Bedoya chose to explore options abroad. In late 2008, he signed a contract with Swedish club Örebro SK and joined the club on January 7, 2009. On April 6, he made his debut for Örebro SK coming on as a substitute in the 73rd minute. He scored his first goal for Örebro SK when he gave the team a 1–0 lead against Assyriska FF in the Svenska Cupen. Over the course of the season, Bedoya worked his way into the starting line-up and became a mainstay at central midfield in Örebro SK 4–3–3 formation. In February 2011, Bedoya was given a trial at English Premier League side Birmingham City, but was not signed.

On December 22, 2009, Bedoya received his first call up to train with the senior United States national team. Training in Carson, California began for Bedoya and the other players called up on January 4, 2010, leading up to a friendly match in Carson against the Honduran national team on January 23. In the 61st minute of this match, when the U.S. was down 3–0 and was playing with ten men, Bedoya earned his first senior cap. Bedoya was named to the preliminary 30-man roster for the 2010 World Cup and played against the Czech Republic in a tune-up friendly, but was cut from the final 23-man roster. He earned his first international start in a friendly against Brazil in August 2010. He was added to the 23-man roster for the 2011 CONCACAF Gold Cup when Benny Feilhaber was unable to play due to an injury sustained while playing for his club team, the New England Revolution of Major League Soccer.

On July 21, 2011, it was announced that Bedoya had agreed to personal terms with Scottish club Rangers, pending the approval of a work permit, with a view to joining in January 2012, once the Allsvenskan season was finished. However, Örebro SK and Rangers agreed an undisclosed fee on August 17, 2011, allowing him to join Rangers immediately.

Bedoya made his debut as a second-half substitute in a Scottish Premier League match against Aberdeen on August 28, 2011. He scored his first Rangers goal in a 5–0 victory over Dundee United on May 2, 2012 to help secure second place for the Glasgow club.

When Rangers entered administration, Bedoya signed a short-term contract with Allsvenskan champions Helsingborgs IF on August 10, 2012. On August 18, 2012, in his debut with the club, Bedoya scored an overhead kick goal in his team’s 2–1 loss to Elfsborg. He started both games for Helsingborg in the home-and-away series against Celtic in the UEFA Champions League; the Swedish champions were eliminated on a 4–0 aggregate. Helsingborg were sent into the 2012–13 UEFA Europa League group stage where they finished in third place and Bedoya scored two goals against Hannover 96 and FC Twente. Bedoya received a number of offers after his contract expired with Helsingborg but decided to stay for at least another six months.

On August 7, 2013, Bedoya joined newly promoted Ligue 1 side Nantes. He went on to make his first Ligue 1 appearance for Nantes against reigning champions PSG on August 25, 2013. Bedoya’s first goal for the club came in Nantes’ 1–0 victory over AC Ajaccio on October 19, 2013 when he scored the only goal three minutes from time to extend the club’s winning run to four games in a row. Following the match, his manager, Michel Der Zakarian, praised Bedoya for his intelligent play and technical excellence. Bedoya scored his second goal for the club, and first at Nantes’ home ground the Stade de la Beaujoire, on December 3, 2013 notching Nantes’ equalizing goal in an eventual 2–1 victory over struggling Valenciennes. Bedoya continued his scoring run on December 6, 2013 netting the game’s only goal in Nantes’ defeat of Marseille, a result which lifted Nantes into fourth place and caused the sacking of Marseille manager Élie Baup. On February 10, 2016, Bedoya scored the winning goal with a header in the 118th minute for FC Nantes in a Coupe de France match against FC Girondins de Bordeaux.

On July 5, 2013, Bedoya scored his first international goal in a friendly match against Guatemala at Qualcomm Stadium in San Diego, California. Bedoya was included in the United States roster for the 2013 CONCACAF Gold Cup, helping the national side to its first Gold Cup championship in six years. Bedoya was part of the United States squad at the 2014 FIFA World Cup and played in all four of the U.S. games.

On August 3, 2016, Bedoya joined Philadelphia Union from Nantes for a reported $1 million transfer fee.

On August 4, 2019, Bedoya scored in the third minute of a 5–1 victory for the Union over D.C. United at Audi Field and celebrated by taking an on-field microphone to say “Congress, do something now. End gun violence,” in response to recent mass shootings in El Paso and Dayton. His statement, which was aired live on Fox Sports 1, resulted in national attention but no punishment or fine from the league. Bedoya also won the MLS Player of the Week for his performance during the match.