The best arcade games like Bomberman 64 are Saturn Bomberman, Super Bomberman R 2 and TowerFall Ascension. Below are 7, each with the reason it is here — and, at the end, what filtering to arcade costs you.
Filtering to arcade means you want short runs and a score, not a campaign. It is the right filter when what you liked was the one-more-go feeling.
What you get: A complete experience in twenty minutes, and a skill you keep. Arcade design is measured in the moment after you lose.
What made Bomberman 64 worth playing in the first place is covered on the full list. This page is the arcade part of that answer, and only the arcade part.
Ten players on one screen, and the best of the 2D entries.
The modern entry, and it still works at four players.
Four players, one arrow each, and the fastest local matches there are.
Four-player arena chaos where the stage is a weapon.
The party fighter with the most staying power.
Grid-based multiplayer sabotage at speed.
The other four-player mainstay of that era.
Story and progression. Arcade games repeat on purpose, and if you want to be pulled somewhere they will not do it.
Specifically, these are strong answers for Bomberman 64 that are not arcade games, so they are not on this page:
The full list is on games like Bomberman 64 — 9 picks, no genre filter.
Saturn Bomberman. Ten players on one screen, and the best of the 2D entries.
No. Bomberman 64 released on the Nintendo 64, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
They were designed to end. A machine that let you play for an hour on one coin did not earn its floor space, so difficulty was the business model.
Constantly, mostly by small teams. Several of the best beat-em-ups and run-and-guns of the last decade are new games built on forty-year-old design rules.
By hand. Each pick was written for the full Bomberman 64 list first, on what the game actually does, and this page is the part of that list that is arcade — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the arcade guide for where to start in the genre generally.