How would we do this if we're to believe this is possible anyways?
The relevant rules say
Manifest Echo
you can use a bonus action to magically manifest an echo of yourself in an unoccupied space you can see within 15 feet of you
So if planes of existence are separated physically by an infinite amount of space, that would mean manifesting an echo in the space of a plane that you could see wouldn't be possible since the distance exceeds the limit.
That would rule out effects that allow you to see the material plane from the border ethereal, such as a potion of etherealness or the spell itself.
What about teleporting back into the plane you travelled from?
The relevant rules say
Manifest Echo
• As a bonus action, you can teleport, magically swapping places with your echo at a cost of 15 feet of your movement, regardless of the distance between the two of you.
In this case distance wouldn't matter, as long as you have that bonus action and the 15ft of move speed.
So say you're in a situation where you want to apply this. You're about to fight the BBEG and you've come prepared with two bags of holding. Your Echo is manifested already so it's your turn and you get within 10ft of them, using a free action to create the gate to the astral plane with 15ft of movement to spare. You're transported there but using your bonus action, swap places with your echo who's still in the plane you came from
Are there rules that don't allow this?
Edit: I've been informed manifesting an echo from the border ethereal has a much more general rule that explains why it is not possible, as stated in the DMG p.48
The Ethereal Plane is a misty, fog-bound dimension. Its “shores,” called the Border Ethereal, overlap the Material Plane and the Inner Planes, so that every location on those planes has a corresponding location on the Ethereal Plane.
Best Answer
This works.
Since there is no challenge to having the echo be 15 feet away from you when you discharge the bag of holding bomb, this just works. You are teleported to the Astral Sea, leaving your echo behind.
All we need to do is demonstrate that your echo is not destroyed when you are teleported. The end conditions for your echo are:
Your echo is destroyed if:
Notably, none of these things happen when you are transported to the Astral Sea via bag of holding bomb. Your echo is destroyed if you and your echo are on different planes at the end of your turn, but that doesn't happen till the end of your turn.
Once you and your echo are on different planes, the first bullet of Manifest Echo states:
As you have proposed in the question.
If the bag of holding bomb is discharged and both you and your echo are in its range, things are a little more tricky. If the echo is not a creature, it is not sucked into the Astral Sea:
Only creatures are sucked into the Astral Sea, so if the echo is not a creature, it remains where it is when the bag of holding bomb is discharged. Once this happens, there is nothing in the description of Manifest Echo that would prevent using your bonus action to teleport, swapping places with you echo as you describe in your question.
However, if the DM rules that the echo is a creature, well you both got sucked into the Astral Sea. So is it a creature? This problem is explored in these questions: Does an Echo Knight fighter's echo provoke an opportunity attack when it moves? and Is the Echo of a Echo Knight actually a creature? There is some amount of disagreement, and I can see merits in either ruling.
So ask your DM.
This sort of ambiguity is quite common with Echo Knights. I've played the class, and been the DM for it, and there are numerous things requiring DM resolution. A few of my answers go into more detail about my experience working with the class. The short version is that the player and DM need to talk frequently and keep track of rulings for consistency.