His jumps should definitely be the zero gravity style Bomberman Hero ones, making him floaty on the way up, allowing him to still drop bombs on people without getting caught in them. Down or Neutral B would therefore be the Bomb Drop. Probably down so that Neutral can be throw.
So currently my specials look like:
Up B - Bomber Jet: Bomberman's rocket pack appears and carries him upwards about 1.5x his own height. During this action, he can be tilted up to 25 degrees in either direction but sadly, bombs cannot be used ¹. On contact with another player, the rockets will explode for small-medium damage and knockback, not harming Bomberman but ending the move. This will also happen if he is attacked, blocking the hit but making him fall.
Forward B - Bomber Skates: Bomberman grabs a small roller skate iconned square from some hidden pocket and suddenly he has skates. They carry him forward at alarming speed, during which time he cannot stop but has his fall speed halved. He will only travel about 2 stagebuilder block lengths before the move ends but, during this time, he will pass through anything but solid objects, impervious to any obstacles below, doing small-medium damage to anyone he passes through, voiding any pitfall traps and instantly triggering any explosives with no harm to himself. Furthermore, if he collides with a foe at the very end of this motion, he will do fairly large knockback, as opposed to the regular, flinching variety. Be careful with this move though, it's easy to fall off the stage and getting hit in the head will result in the character being downed.
Neutral B - Bomb Toss: If there is a grabbable item infront of him, Bomberman will pick it up, otherwise the move will spawn a bomb for him. After a charging period, the item, whatever it may be, will be thrown in an arc and destroyed on contact. This means explosions if it's a bomb. Since it involves an item, however, the move may be stopped with a well timed grab or, more interestingly, it could potentially go infinite with two bombermen ² and a non-bomb item.
Now for the charge. While Bomberman's bombs and links are pretty much the same (maybe even interchangeable, who knows), Bomberman has the ability to pump his up. This is done by holding the button down during this special item throwing move. You see, rather than affecting the damage and knockback properties of the move itself, the charge comes in 3 stages. Un/barely charged leaves the bomb as is, merely pausing the countdown for the brief period in which Bomberman is holding it. Partially charged replaces the bomb entirely, giving him a bigger, better one (countdown reset). Greatly charged pumps it up to full strength, again, replacing the medium bomb. The new item has a P on it just because. These bomb changes affect both knockback, damage and range of the explosion. Medium bombs, if caught and used for this move, will only change when the pumped up bomb would otherwise be produced.
With each charge stage, the item trajectory will change to mimic the way bomb weight affects his throw in the games. Note that this will happen regardless of what item the white bomber is actually holding. Finally, fully charging the move will cause whatever item he has to glow red and be thrown immediately, with a distance a tiny bit further than that of the normal pumped up bomb throw but not really worth the extra wait.
Down B - Bomb Drop: Bomberman will spawn a bomb that is much like (or perhaps even the same as) Link's. If he is on the ground, he will literally lay it, otherwise he will go into a sitting pose and have it appear in his hands, only for him to drop it as he restraightens his little bomber legs. Either way, it is a quick move, with the aerial version being just a tad slower.
Extra Note: Any one Bomberman may not have more than 2 bombs out at any one time ³. Attempting to spawn another will instead spawn a small puff of grey dust, as it does in some Bomberman games. This is not, in any way, to be considered a fart.
The bomb kick and similar would be a result of his non-special moves being used on the bomb spawned by the Bomb Drop.
¹ No, he doesn't use bombs with the jet in game, those are actually the same torpedoes he has in the Bomber Sub.
² Bomber Kirby is not a viable bomberman substitute since his lower shoulder height drastically affects the range of the move.
³ 2 because it is what Diddy is limited to with his bananas and also because, in games where he has more than one bomb to start, it is the lower limit for Bomberman's bomb capacity.