This is basically the same post I made previously, but this time I'll add some images. I know nothing about Bomberman's canon as I only play the multiplayer mode in all the games.
Forward Smash:
The angle is too low, he's basically attacking the floor, and the hitbox goes away too fast, which makes sweetspoting with the bomb too hard.
Compare to mario, his FSmash is a straight attack (can be angled, but let's talk about the regular C-Stick version here). Using a similar animation to this one, the bomb sweetspot can be landed easily. I don't know if the current one is a canon move of his, but...
Up Special:
Without a charge, it's pitifully bad. Fully charged it has a pretty good range. Having a charged bomb at all times to use the better move is a pain, and it may lead to reduced use of his Neutral B bombs.
Now, there's another thing that makes this bad, because his uncharged move is comparable to C.Falconl's, and that issue is the forced forward movement. I used the UpB in the purple line in the screenshots, but no matter how much you hold back after the input, he will still move forward. This leads to him getting stuck under platforms when he's too close to the stage, and makes his recovery too predictable.
Down Smash:
Is there a reason why it has no reach at all? In the screenshot here (it got corrupted somehow), Mario and Bomberman are standing at the same distance in both screenshots, but Bomberman's DSmash can't hit Mario. And Mario's DSmash is more useful too...
DAir:
Now this move is one of the most useless he has right now. I guess you can use it to land safely, but...
If used offstage, he will SD 100% of the time, and the DMG/KB this does is nonexistent. The opponent can just jump out of it. Bye Bomberman!
Using it on the ground isn't any better. When he touches the ground, he produces an explosion, with good DMG/KB, but it still won't kill anyone. After a certain percentage, depending on the character, the first hit will push foes away from the explosion...
My earlier suggestion was to make the explosion trigger in contact with the opponent and stop his momentum/animation/whatever, so he can save himself after using it. The explosion can also have a Meteor/Spike hitbox too, why not?
FAir:
Hitting with this is harder than it should be, it needs a bigger hitbox and lower kick angle. Also, you can't even Shorthop>FAir with this, only if you SHFFL. Not terribly necessary, but it would be a lot more useful.
Side Special can be jump cancelled if you have a jump left, but it would be a lot better to make it possible to use UpB after this, exacly like Luigi, but if his regular UpB is getting changed then this may not be needed.