Atomic Punk (Game Boy)
This is indeed a Bomberman game, just with a different title. It even has a special mode based on the NES game! It's also the first Bomberman game to have a battle mode (called "VS.MODE")!
In the normal game mode (GAME A or BOMBER BOY), at the STAGE SELECT screen, enter the MY TOWN location with Right + Select + B + A held. Note, that when you press Right a map selection is changing, so you need either to put it to the left of the MY TOWN before holding all the buttons, or press Right until you stand on the right one position and hold it there, and then hold the rest of the buttons.
In the Japanese version, the mode based on the NES game appropriately changes the title screen to Bomberman.