He started out at as a senior at Baia Mare teams FC and FCMU, before moving to FCM Târgu Mureș at age 17 to record his Liga I debut. After a loan spell at Roma Primavera between 2012 and 2013, Bumba returned to the then-renamed ASA Târgu Mureș for two additional years. Since leaving the latter, he went on to appear for sides in Israel, Turkey and Hungary, apart from stints in his native country.
A former Romania youth international at several levels, Bumba earned his first and only cap for the full side in 2012, in a 4–0 friendly victory over Turkmenistan.
Bumba moved to FCM Târgu Mureș of the Liga I in June 2011.[2] On 22 July that year, he registered his debut in the competition in a 0–1 loss at Dinamo București,[3] and on 15 October scored his first league goal to earn his side a 1–1 away draw at Sportul Studențesc.
In February 2012, former Târgu Mureș manager Maurizio Trombetta confirmed that Italian team Udinese was monitoring Bumba.[4] On 25 March, he netted in a 2–0 win over Astra Ploiești.[5][6] In May, he was included by website and TV channel Sport.ro in a top ten list of Romanian youths to watch.[7] Bumba finished his breakthrough season in Târgu Mureș with three goals from 29 appearances, but his performances could not help his team avoid relegation to the Liga II.[8]
In the summer of 2012, Roma paid €600,000 to loan Bumba for one season.[9] On 6 September, after recovering from an injury, he scored for the under-19 team in a 2–1 defeat of Inter Milan in the Supercoppa Primavera.[10] Bumba returned to Târgu Mureș in July 2013, after the club changed its name from "FCM" to "ASA 2013".[11]
On 11 January 2015, Bumba penned down a three-and-a-half-year deal with fellow Liga I club Astra Giurgiu,[12] but after less than a month returned to ASA Târgu Mureș due to a breach of contract.[13] He amassed 31 appearances and eight goals during the 2014–15 season, as his team finished second in the league championship with only three points behind FC Steaua București.
Bumba featured in 31 games and scored two goals in all competitions during his first campaign in Israel, as Hapoel finished ninth overall in the national league. In the winter of 2017, he chose to leave the club because of unpaid wages.[16]
Dinamo București / Concordia Chiajna
In February 2017, after a move to CFR Cluj fell through,[16] Bumba returned to Romania by signing a two-and-a-half-year contract with Dinamo București as a free agent.[17] He scored his first goal for "the Red Dogs" on 10 April, in a 2–1 league win against Astra Giurgiu.[18]
Bumba won his first major trophy on 20 May 2017, following Dinamo's 2–0 defeat of ACS Poli Timișoara in the Cupa Ligii final,[19] despite not making any appearances in the competition throughout the season. On 24 August, the club announced the termination of Bumba's contract on a mutual agreement,[20] and one month later he moved to Concordia Chiajna.[21]
On 27 September 2017, less than a week after joining Chiajna, he made his debut and netted in a 3–2 Liga I win over his previous club Dinamo București.[22]
Adanaspor
Bumba changed countries again on 20 July 2018, after agreeing to a two-year deal with Turkish team Adanaspor.[23] He contributed with three goals from 27 appearances during his first and only campaign in the TFF First League.
Kisvárda / Fehérvár
On 19 July 2019, Bumba signed for Hungarian club Kisvárda on a two-year contract with an option for another year.[24] He made his debut on 31 August, entering as a 64th-minute substitute in a 0–3 Nemzeti Bajnokság I loss to Fehérvár.
On 24 June 2022, Bumba was formally unveiled as a Fehérvár player after agreeing to a two-year deal with the team.[25]
Bumba has partial Hungarian heritage through one of his great-grandmothers, as he revealed in August 2021. In the same interview, he also stated that he considers taking up Hungarian citizenship after not being called up to the Romania national team in several years.[29]
^"România debuteaza contra Cehiei la CE U17" [Romania debuts against the Czech Republic at the U17 European Championship] (in Romanian). Sport365.ro. 2 May 2011. Archived from the original on 1 October 2011. Retrieved 24 April 2022.