Bedman's Existence
Since Ken Miyauchi (Guilty Gear Strive Producer) confirmed that a portion of Bedman's soul (or spirit) is in the bed, I can't help but wonder if this also indicates that Bedman couldn't cross the afterlife, and therefore, still lingering elsewhere.
Though I personally believe that they initially want Bedman's existence to be ambiguous except for "this bed could be haunted," this interpretation could also imply that Bedman is somewhat present, like a ghost.
And the thing is, there's a character who was implied to be unable to move on to the afterlife because of having only half a soul, that being: Raven. Daisuke mentioned that the coin in Raven's left eye symbolizes having only half a soul (based on an uncommon interpretation of Greek tradition that both eyes needed to be placed with coins (specifically Charon's obol) during burial so that the spirit can cross the underworld).
Therefore, if a portion of Bedman's soul is in the bed, then his soul (wherever it is) was basically incomplete. And if the logic from Raven's case will be followed, then... BEDMAN IS ALI-
However, there were still some problems:
1) Will they follow that part of Raven's lore?
Retcons happen, though the fact that they maintained the coin design in Xrd improved the chances of keeping this lore. But unless they release Raven in Strive, the details were still up in the air.
2) Bedman is nowhere
It wasn't the first time for Guilty Gear to tackle the concept of souls. From the formation of Magical Foci, Zappa's ghosts, Happy Chaos' possessions during the Crusades, REI possessing Giovanna during fights, and now Lucy's existence in Guilty Gear (though still possible to be a forced explanation) all had something to do with souls, spirits, or ghosts. However, deleting his ID complicates the situation since aside from being a soul, it also turned him into a multi-dimensional being, which are closer to GG's vampires and werewolfs.
And since (to my knowledge) there isn't much information about multi-dimensional beings in general (probably because they just introduced the concept in Happy Chaos' arcade story), then it is hard to draw a conclusion on what could happen to him as both a multi-dimensional being and a soul in an unknown location. (Like, does the soul still act like a soul or a multi-dimensional being? If the soul is located in the Backyard, then it's prone to becoming a Magical Foci. But if it's near the afterlife, can it leave that area as a multi-dimensional being? There's too many possibilities).
But let's say his soul is just, out there somewhere, just staying still. Maybe someone can find him? Asuka perhaps? But again, his multi-dimensional nature may make it difficult to find his soul (in wherever he is) due to his lack of ID. It's probably like looking around blindly in the vast universe. Also, aside from the soul...
3) Bedman's body
Raven still has a body when he gained immortality, Bedman on the other hand...
And based on Happy Chaos' explanation of (naturally born) multi-dimensional beings, they need to convert themselves into lower levels of information before having a physical body (at least, that's how I understand it). But since Bedman already lost the "converted version" of his body (that is, one that was already compatible with their world), he may no longer have the information/matter/unit needed to have a proper physical form (unless he steals it from other worlds, but it's not like he can do much as a soul, and I doubt he'll let the other Delilah without a brother nor steal someone else's body).
So in order to physically return Bedman back to their world, Asuka would have to either create a new body, or use that unfinished Happy Chaos unit. However:
4) How will they handle his power?
His body will also need to be able to sustain Bedman's extremely high brain processing power. Delilah was only cured because of Bedman's omnipotence in his temporary Absolute World, but without that, will Asuka be able to find a solution for him? We certainly wouldn't want Delilah to die like he did just so he could live.
However, this was less of an issue given how Asuka also held the Tome of Origin, and how they could always come up with a new magical/physics rule to make it work... If they want to make it work.
5) Will he still have a narrative purpose?
His story represents a classic tragic tale. If they are going to turn back from that, it must be for a very good reason. Question is, for what? If things go south, they can make Asuka voluntarily come back to earth, Happy Chaos can call I-No, and Delilah is already stronger than Bedman. So, what else will Bedman bring?
At most, Bedman's greatest asset was his fast thinking and ability to create his own Absolute World. Without limitations, he may be able to counter a god-like being. At the very least, his mind can be used by someone other than the main cast for evil or "supposedly good" purpose (though that's adding more salt to the tragic angle, and that might make it distasteful if overdone). Regardless, I think it has to be an enemy so great to require another overpowered back-up, but too great and the series will not have much conflict left to continue the story. And that might place his speculative comeback further into the end of the series.
So, in summary:
Should they follow Raven's lore where incomplete souls are immortal, some sort of miracle must happen for them to even find Bedman. That may be Giovanna's heightened smell, Slayer's intervention, Asuka using the Tome, there's a lot of possibilities. But he's been introduced as an overpowered character with limitations, so bringing him back (with or without limitations) would also require a problem that is just as big.
Either way, one thing's for sure: Bedman is still there somewhere...