Career
Baia Mare
Bumba made his league debut in a 1–1 draw against Gaz Metan CFR Craiova on 10 October 2009, at the age of 15, playing for Football Club Baia Mare. In the summer of 2011, he moved to Liga I side FCM Târgu Mureş. Târgu Mureș
On 22 July 2011, Bumbă made his Liga I debut in a match against Dinamo Bucureşti, at the age of 17.
In October 2011 he scored a goal in a game against Sportul Studențesc to earn a draw for his team
On 25 March, in a game against Astra Ploiești, Bumba opened the score in the 44th minute. The game ended in a 2–0 victory for Târgu Mureş, with Andrei Cordoş scoring the second goal.
In March 2012 it was confirmed by manager Maurizio Trombetta that Udinese is monitoring Bumbă. In May 2012, after continuous good plays, he was included by Sport.ro in a Top 10 list of Romanian youths to watch.
He was mentioned alongside names like: Vlad Morar and Nicolae Stanciu.
Bumba finished his breakthrough season at Târgu Mureş by putting in 29 appearances and scoring three goals. His good plays couldn"t help his team avoid relegation to Liga II, as they finished 15th out of 18. Loan to Roma Primavera
In the summer of 2012 Roma paid €600,000 to secure Bumbă"s services on a one-year loan deal.
Return to Târgu Mureș, failed move to Astra Giurgiu
In July 2013, Bumbă returned to Târgu Mureș, where he found a new team, after FCM changed its name to American Statistical Association. On 11 January 2015, Bumbă signed a contract for three and a half years with Astra Giurgiu.
After less than a month, Bumba returned to American Statistical Association Târgu Mureș due to a breach of contract. Hapoel Tel Aviv
On 19 June 2015, he signed a four-year contract with Israeli club Hapoel Tel Aviv.