When I originally bought the game in 1999, I enjoyed it and played it a fair bit, but after putting it away after getting stuck at the Beach Zone, I didn't think much of it after that. Having played it, completed it, and turned it all around, I can definitely say it's one of the best single-player Bomberman experiences I've had.
While multi-player Bomberman has always been simple and enjoyable with only a few minor exceptions (Quest sadly being one of them), single-player has been a tough cookie for Hudson to master. The "destroy all enemies" concept has been used most often, but it only becomes slightly fun when you've got friends assisting you; the "destroy the switches/crystals/generators/whatever" one also suffered the same problem. Bomberman 64 brought some freshness in by making it so you have to open and locate the exit, but at the expense of them being hellishly long.
Bomberman Quest takes the "destroy all enemies" gameplay, but makes it so it isn't necessary, while throwing in a few minor RPG elements. Some baddies will have items required to finish the game, while some will provide you with less useful equipment; the main deal is beating the bosses, which allow you to progress further in the game, and thus encounter more enemies, and in turn get more items.
Of course, fighting the enemies is more fun because it's one-on-one, and they're generally more tactful than in the regular games. And instead of fighting in the typical "every other tile is a hard block" arena, you're in a real world map, with other obstacles such as pits, spikes, trees and rocks. If there's a downside to the fighting, it's that with the right combination of items (Homing Bomb and Power Gloves), you can easily thwart just about every enemy in the game with no difficulty. Or you could simply not do that. Your choice.
The game is very short with only four areas, although the fact it's easy to pick up and play is a plus, and the three secret bosses may add a bit of replay value, but after everything is done and dusted, that's it. There isn't a rearranged quest to mix things up, and despite being very simple and just begging for one, nobody has bothered to make a level editor for it. And I'd love to see what's hidden inside the data.
To summarise, ja, incredibly fun game while it lasts, and I highly recommend giving it a shot, even if the replay value is limited. Make the most of it.