Hey! I didn't read the other comments because there seemed to be alittle bit of negativity going on so I'm bypassing that - sorry if my advice has already been said!
First of all, he's very cute :) What breed is he, just out of curiosity? In one of those pics he looks like he would not be that comfy bareback, haha!
As far as critique; the biggest thing to remember when working towards "on-the-bit" is that it has to come from his HIND end, not the front. On the bit is kind of a silly term, IMO, because it implies that the head is the focal point. I think a much better term is "on the aids" and I wish that was taught more! What you have to get him to do is hold your hand while coming with impulsion from behind - so you want a steady contact, but not a pulling one, and you want to use your legs and seat to get his hind end really active. One of my trainers once told me to get my horse to 'extend behind, collect in front.' Sounds silly, but that mental image did the trick - I really put my leg on until that hind end came under, and then half-halted so the front end elevated. Then the horse naturally went into self-carriage.
Working on the aids is a long process - like all training! You seem to be really dedicated to your horse and your riding, so I'm sure you guys will progress just fine
You're on the right track, just tweak your approach a little! Hope my tips weren't too cryptic...lol!