[2] Bogdanović began playing organized football at the age of twelve, getting invited to try out for hometown side Željezničar's youth system in June 1982 after being noticed at a local primary school tournament by the club scout and former goalkeeper Ruda Bulić.
[3][4] After passing the tryout, Bogdanović was attached to the Željezničar cadet (under-16) squad coached by Duško Bajić; among the youngsters joining the club's youth system at the same time was Goran Gutalj.
[3] By spring 1987, the teenager was set to make his full squad debut away at NK Osijek on 24 May 1987 due to the team's established defensive midfielder Edin Ćurić serving a one-match suspension for an accumulation of yellow cards.
However, a medial collateral ligament (MCL) injury—sustained four days earlier during the SR Bosnia-Herzegovina provincial youth (under-18) cup final versus FK Sarajevo under-18s—forced Bogdanović into a six-month layoff that included surgery followed by months of regaining match fitness.
[3] Recovered from knee injury and surgery, teenage Bogdanović was attached to the Željezničar full squad under manager Blagoje Bratić in January 1988, joining players such as Dragan Škrba, Branislav Berjan, Mirsad Baljić, Vlado Komšić, Edin Bahtić, Edin Ćurić, Zoran Slišković, Edim Hadžialagić, Radmilo Mihajlović, and Milan Pavlović with the team stuck in the bottom half of the table throughout the league season.
[3] Entering the contest in the 65th minute with visiting Željezničar up 0-1, Bogdanović was brought on in an effort of protecting the lead, however, the match ended 1-1 as Dejan Savićević tied the score for the home team.
[3] The offseason also saw the return to the club of the thirty-two-year-old fan-favourite veteran Nikola Nikić after four seasons abroad as well as the acquisition of young winger Simo Krunić from the Second League team Famos Hrasnica.
After one of these training sessions [with the FK Partizan squad] at the JNA Stadium in Belgrade, Goran [Gutalj] and myself got approached by a guy named Fakrija Šekularac asking us if we’d be interested in transferring to the Korean league.
The twenty-two-year-old fled to Belgrade along with several other Željezničar first team players such as Simo Krunić, Gordan Vidović, Suvad Katana, Siniša Nikolić, Srećko Ilić, and Jasminko Velić.
With the Yugoslav up front and twenty-three-year-old Korean rising star Hong Myung-bo in defence, POSCO Atoms edged out Ilhwa Chunma from Seongnam to win the 1992 K League title.
Bogdanović was hoping for a compensation agreement with JEF that would allow him to go stay with Ajax's talented squad featuring Edwin van der Sar, Danny Blind, Winston Bogarde, de Boer brothers (Frank and Ronald), Richard Witschge, Marc Overmars, Tijani Babangida, Jari Litmanen, and Patrick Kluivert, but the UEFA arbitration committee got involved and the twenty-six-year-old was forced to honour the contract he had signed in Japan.
Unbeknownst to Bogdanović at the time, while training with Ajax in La Manga, he was noticed by the Atlético Madrid assistant coach Rešad Kunovac who was there on a scouting trip assessing the Dutch team, his club's next opponent at the upcoming Champions League quarterfinals.
With Atlético taking a 5-2 advantage into the return leg in Thessaloniki, Vieri was again rested by Antić while Bogdanović started and got a goal in the high-scoring contest that ended 4-4, his very first European continental club match.
Back on La Liga front, Vieri got injured minutes into the next league match, at home versus relegation-battlers Compostela, with Bogdanović coming on and scoring before making way for Vizcaíno at halftime.
[17] Three days later, with Vieri still not fully recovered, Bogdanović began the league match versus league-leaders FC Barcelona at Camp Nou in front of 80,000 spectators before being subbed off fifteen minutes into the second half with the score tied at 1-1; Barça won 3-1 by the end, dropping Atlético to sixth in the table.
As a consequence of finishing the preceding La Liga season in disappointing 7th spot, the Madrid club management undertook a major squad rebuilding effort during the offseason with coach Radomir Antić fired and Arrigo Sacchi brought in.
[27] Without naming specific names, in various print interviews throughout mid-to-late 2010s (some 20 years after the alleged event), retired footballer Bogdanović has made claims about having been offered a spot on the Yugoslavia 1998 FIFA World Cup roster in exchange for paying DM50,000 as part of an alleged pay to play scheme: "After my [summer 1997] Atlético transfer, which I had completed without an agent, I got a call from a well-known Yugoslav coach who had gotten my number through [Atlético head coach] Radomir Antić.
Commenting on poor defending by Borussia Dortmund in a Champions League match against FC Barcelona, he stated that the German team never recovered from manager Lucien Favre's past decision to "play with four blacks in the defensive back line towards the end of the previous Bundesliga season".
[29] During the coverage of the same game, Bogdanović further commented on Barcelona's €150 million signing Ousmane Dembélé's time at the Catalan club by claiming that "the Barcelona people hired a nutritionist for the kid to explain to him that he shouldn't be eating fast food before hiring a psychiatrist for him to make him aware that watching porn and organizing online gaming tournaments until early morning isn't a proper lifestyle for a professional footballer" before adding that "the renovation of the Clinical Centre of Serbia costs as much as this guy".