Okay, so here I'm going to put my thoughts on Bell's leveling so far, and theories/predictions of him leveling up in future parts of the story, and some things I would like to see happen.
Bell has incredible potential, that is obvious, and considering how quickly he has reached Levels 2 & 3 (a month and a half, and one month) I do expect him to reach future levels in similar timeframes. I think he will reach level 4 in max 3 months of story time (from when he reached level 3). I assume he'll reach level 4 before he reaches the 30th floor, maybe before the mid-twenties acrtually. This seems accurate to me because there are many monsters much much more powerful than him that he can encounter has beat, and (other than those possibly resulting in special codnitions being met for a level up and rank ups) that along with other things means that, as Bell's skills grow he is going to get more confident and each time he gets closer to his goal he will probably keep wanting to get more powerful and thus closer and closer to it, more and more.
Now as for when he does eventually catch up to Aiz's level (I'm guessing that will be somewhere around 1 year though maybe sometime later in the story's time) I'm assuming he'll find a new goal to reach. That goal in my opinion will be him defeating the One-Eyed Black Dragon that defeated the Zeus Familia. Now I doubt that there will be much content after Bell eventually defeats it (hoping there will be, though that depends on what kind of things will happen after obviously), but I do want to see Bell conqeor the Dungeon. Not sure if that would probably happen before or after though, then again its not known what floor the One-Eyed Black Dragon was on (other than the fact that it was in the deep floors) so maybeit was the most powerful monster. Also I think that Bell has so much potential partly because he may be descended from the Zeus Familia. But even then I do think he would be considered very special with an incredible amount of potential even by Zeus Familia standards.
As for Bell's Development Abilities, I believe that his current ones will level up and he will get atleast 2 or so more (though I have no idea what they could possibly be). I'm very interested to find out the benefits of Abnormal Resistense beyong Rank G, and what improved Luck will bring about. I also expect Bell to get more rare Skills, not a lot more but maybe a few or so at most, though this is mainly just something I would like to see.