Anastasios came through the youth system at Asteras Tripoli, and was promoted to the first team in the 2010–11 Superleague season, for which he was assigned squad number 12. He made five league appearances for the club in this season, four of which were as a substitute, and two in the Greek Cup. His Superleage debut was in a starting position against Xanthi on 28 November 2010, a match Asteras Tripoli lost 2–1 despite taking the lead.
In the Greek Cup, he made his first start in a 1–0 defeat to Olympiacos on 22 December 2010. His final appearance for Asteras Tripoli in the 2010–11 season came as a second-half substitute in a 3–0 league defeat against AEK Athens on 16 January 2011.
At the end of January 2011, he went on loan to Thrasyvoulos in the second tier Greek Football League. He played ten league games for Thrasyvolous, scoring his first senior goal against Ethnikos Asteras in a 2–0 win on 28 February 2011. He returned to Asteras Tripoli at the end of the season in July 2011.
At the end of December 2013, he went on loan to Aris to try and help them to avoid relegation. He made his debut to his new team in an away loss from Levadiakos scoring two goals in a 4–3 defeat. He scored another goal before his loan finished. Unfortunately he couldn't help the side avoid relegation.
On 28 January 2015, Bakasetas signed a two years' contract with Panionios for an undisclosed fee. He started the 2015–16 season in amazing fashion scoring 2 goals in the opening 3 matchdays including the winner against giants Iraklis and Panathinaikos. On 17 October 2015, he scored the two goals of his club in a 2–0 home win against Kalloni On 12 March 2016, he scored a hat-trick in a home win against Xanthi. On 3 April 2016, he had a free-kick smashing the woodwork and scored a brace in a 3–1 home win against PAOK, helping his club to seal the European qualification for the next season.On 23 May he was left out of the squad for a match against PAOK,after his denial to join Olympiakos, which is known to buy young players and destroy their careers.
On 28 June 2016, Bakasetas signed a three-years contract with AEK Athens after an agreement was made with Panionios, the transfer fee is believed to be in the region of €300,000. On 17 September 2016, he netted the first goal with the club in an away 2–0 win against Veria. On 9 April 2017, Bakasetas scored a brace in a 5–0 home win against Kerkyra.
Anastasios has represented his country at youth international level. He was selected in the Greece under-19s squad for the 2011 UEFA European Under-19 Football Championship along with Asteras Tripoli teammate Nikolaos Skondras.
He made his under-19 debut in one of the two opening games of the tournament, as a 55th-minute substitute in a 2–1 defeat against the Republic of Ireland under-19s on 20 July 2011. He made his first start in the second group game, a 1–0 victory against the Romania under-19s on 23 July 2011.
On 19 May 2016, was called up for the friendly matches matches against Australia on 4 and 7 June 2016. On 4 June 2016, he made his international debut as a substitute, in a 1–0 friendly loss against Australia, when Mathew Leckie has scores with the final kick of the game to help the Socceroos beat Greece.