The most reliable way to play today is through official "Arcade Archives" or "S-Tribute" releases, which offer modern features like save states and online leaderboards.
For those looking for specific older versions or community-preserved files: Puzzle Bobble™2X/BUST-A-MOVE™2 Arcade ... - Steam
Searching for a leads to several modern and retro options, as this 1995 Taito classic—also known as Bust-A-Move 2 —remains a staple of the puzzle genre. Whether you want to play on a modern console, PC, or revisit the original arcade experience, there are multiple legitimate ways to access the game. Official Digital Downloads (Modern Platforms)
Available as part of the ACA NEOGEO series or the S-Tribute collection on the PlayStation Store.