*Club domestic league appearances and goals, correct as of 08:16, 20 May 2024 (UTC) ‡ National team caps and goals, correct as of 21:48, 21 November 2023 (UTC)
Bułka began his career in his native Poland, playing in the youth ranks at Stegny Wyszogród, MDK Król Maciuś Club Płock and FCB Escola Varsovia, an official Barcelona satellite academy in Poland.[3] In March 2016, whilst at FCB Escola Varsovia, Bułka underwent a trial with Barcelona, before trialling at English club Chelsea the following month.[4]
In the summer of 2016, Bułka joined Chelsea. In September 2016, he signed his first professional contract with the club as well as making his under-18 debut for in a 4–2 win against Arsenal U18. Was highly rated by some fans but nothing prevailed.[5]
After his contract at Chelsea expired, Bułka signed for Ligue 1 club Paris Saint-Germain on a two-year contract.[6] On 30 August 2019, he made his debut for the club, keeping a clean sheet in a 2–0 win against Metz.[7]
Bułka made his first and only appearance for PSG in the 2020–21 season in the first match of the campaign on 10 September 2020, which was against newly-promoted Lens. With Keylor Navas and Sergio Rico absent, he would play the entirety of the match, but made a costly mistake that handed Lens a 1–0 win.[8]
On 28 September, Bułka signed a contract extension with Paris Saint-Germain until June 2025. He was immediately loaned out to Spanish Segunda División club Cartagena.[9] Eventually, his loan was cut short, and he left in the January transfer window.[citation needed]
On 31 January 2021, Ligue 2 club Châteauroux signed Bułka on loan until the end of the season.[10] He made his debut in a 4–0 win against Chambly on 2 February.[11] However, in late February, he suffered an injury to his right ankle, ruling him out of play for "several weeks" according to the club.[12] Bułka made his return to play in a 1–0 loss to Toulouse on 17 April.[13]
On 5 August 2021, Bułka joined Ligue 1 side Nice on loan with an option-to-buy.[14] During the 2021–22 season, he played in all of the club's Coupe de France matches, and one league match against Clermont. On 1 June 2022, his move to Nice was made permanent.[15]
After previously representing Poland at under-18 and under-19 level,[16][17] on 6 September 2018, Bułka made his under-20 debut for Poland against Italy in a 3–0 loss.[18]
On 7 June 2024, he was selected in the 26-man squad for UEFA Euro 2024 as a third-choice goalkeeper behind Wojciech Szczęsny and Łukasz Skorupski,[21] and remained on the bench for all three of Poland's fixtures at the tournament.[22]
On 27 May 2020, Bułka was involved in a traffic collision near the town of Wyszogród, Poland. He was driving a rented Lamborghini on a motorway and collided with an individual driving a Hyundai in the opposite direction while attempting an overtake maneuver. A 56–year old man was injured during the crash and suffered several fractures, while Bułka was left unharmed. Bułka admitted responsibility for the collision. It was reported that he could face up to three years in jail after potentially breaking article 177 of Polish law.[23]
