I'm unfamiliar with the Bomber King games; all I know is that Hudson's official Bomberman game list has the first instalment, but doesn't have the second one, though wasn't the Game Boy one developed by another company? That's probably why.
I admit my collection of Bomberman games is pretty lacklustre. They're all European games are probably missing most of the boxes and manuals, starting from the Game Boy era; the most exciting it gets is Bomberman Kart, which I managed to get on eBay for something ridiculous like £3 or £5, in a time when its rarity demanded the likes of £20 upwards.

I'm pretty pleased with my B-Daman collection, though!
18 keychains (one not pictured since it's with my keys!), two larger translucent figures (not pictured, in storage somewhere) and four even larger show-accurate figures, with removable helmets! I got these on Yahoo Auctions from Malayasia about a decade ago; I can't remember the price, but I imagine it wasn't pleasant. I'm disappointed I haven't kept them in the best shape over the years; as you can see, three face stickers have fallen off, six of them are missing their bobbles, the large Shirobom is missing his marble, and in general there's a fair amount of wear and tear going on. Still, they're nice to have!