The author has an eratic writing pace, so the release of a book will varies depending on how difficult Omori has writing it & the time at his disposition because he is also on other projects, he can release the next MS volume within 6-10 months or take almost 2 years to complete a certain arc (Freya).

Take your time, it's only been 2 books since Bell reached level 5 & the gap between his rank up was always at least 3 entires books. Even in the possibility that Volume is another From Mid to SS & SSS Volume like was 6 & 11, the rank up would only be announced in the next volume so at least volume 21.

We know he received a status update in Chapter 2 of Volume 19 but nothing is mentioned so we are still left with the war game stats so his highest stat is F for Endurance & Agility.

Oomori's writing speed is influenced by the anime. DM16, the first to take quite a while, coincidentally was released the same month Season 3 aired. Then we got DM17 just six months after (normal pace) but for DM18 we had to wait almost two years, volume which just so happened to be published the same month as Season 4 Part 2.

Personally, because of it, I am expecting a new volume releasing around Season 5's airing. Just speculation on my part though.

As for Bell's next rank up, he has spent: 3 volumes as Level 1, 3 volumes as Level 2, 5 volumes as Level 3, and 6 volumes as Level 4. So he is going to remain a Level 5 for probably another three volumes. And then he won't actually rank up until the start of the next volume, so we'll likely have to wait until volume 23 at least.

The amount of volumes per level has been increasing until now, so if that trend continues Bell will be at level 5 for more than 6 volumes.

I doubt that he will level up in this arc, so another one will be needed for this purpose and since Omori likes 3-volume arcs, there could be 1 or 2 more volumes referring to the school district and another 3 more for the next arc, which would give a total of 6 or 7 volumes for this level. So, Bell will be leveling up in volumes 24 or 25.

Of course, this speculation is based on Omori's tendencies to increasingly increase the number of volumes per level and the constant of 3 volumes per arc. He might change things by making 2-volume arcs for example, to shorten the times, but is there any indication to think that that will be the case?

It’s already confirmed that School District arc is a two volume arc that ends in Vol 20. Bell most likely will reach Lv6 no earlier than Vol 25 so after the School District arc there should be two more arcs before Bell becomes Lv6.

Not sure what the first arc after the School District arc will be about but I think the second one will be the Ais arc. Bell will be seen as an equal to Ais when he reaches Lv6 so this should happen after the arc or during the climax of the arc.

An arc with Ais mmm... there are complications about it, it would be feasible if the power of both were moderately leveled but that is not the case. Omori decided to weaken Bell, he is no longer the one who could face opponents with a higher level than his, since he rose to level 5 Omori has reiterated that he is absolutely inferior to all other level 6s; In contrast to this he has super strengthened Ais, through her black wind (tempest-avenger) she is as powerful as a level 8 at least. Both facts have generated an abysmal difference between the two, of up to 3 levels.

If the adventure will be against monsters, I don't see how Bell could be useful to Ais due to what was previously explained, of course, Omori can always resort to power inflations, as he did with Mikoto against the Bringar, she went from not even being able to perceive who nor that attacked her to be so effective as to catch the 4 of them in motion with her magic and even personally defeat one of them, however, these power inflations are something very unpleasant.

Nevertheless, the collaboration between both of them would make much more sense if the antagonists of the arc were people instead of monsters, thus Avenger would be removed from the equation, eliminating the biggest gap between them. Furthermore, Ais is the best monster matcher but she is not a great duelist, so, if the combats will be in duel mode, it is very reasonable that she would need help from someone like Bell for such a challenge.

Both alternatives are controversial in some sense, but between inflating Bell's power by 3 or more levels or introducing new powerful antagonists, I prefer the second option.