Naruto
Bleach and Naruto are constantly recommended together because they are both major long-running battle shounen with rivalries, training arcs, transformations, and huge casts. Naruto leans ninja and emotional backstory, while Bleach leans spiritual swords and style, but the audience overlap is obvious.
Jujutsu Kaisen
Jujutsu Kaisen feels like a modern spiritual successor in many ways: exorcist-style fighters, cursed monsters, stylish mentors, and ability-based battles. Fans who like Bleach's Soul Reaper world and cool-factor combat usually find JJK very easy to enter.
Yu Yu Hakusho
Yu Yu Hakusho shares supernatural fights, spirit-world rules, tournaments, and a delinquent hero pulled into a hidden realm. It is older and more compact, but it carries a lot of the same spirit-battle DNA Bleach fans enjoy.
D.Gray-man
D.Gray-man overlaps through exorcists, cursed weapons, gothic enemies, and a long war against supernatural forces. It is darker and more religiously styled than Bleach, but the organization-versus-monsters structure is familiar.
Soul Eater
Soul Eater shares stylized supernatural combat, weapon-based partnerships, and a world where fighting evil spirits is built into the setting. It is more cartoon-gothic and school-based, but the visual flair and soul/weapon themes appeal to Bleach fans.