Bushido is an incredibly low mana cost magic. I don't see your MR listed, but I will assume you have given the pet MR. You also have 370 Int, 115 Med, 100 Focus, so it will have good mana regen overall. I have a Bushido/FWW Hiryu and he is hard pressed to spend 100 mana just due to the cheap cost of his spells.
As a side-note though, this is
not due to some mystical innate super mana regen ability that Hiryu/Lesser Hiryu have (as
some might still have you believe). We have tested the mana regen of all the major tamable pets and they all regen in line with the mana regen formula.
There may be an issue with Hiryus where they try to use the Dismount ability (even though its not a valid target, i.e. non-mounted mob). This ability attempt doesn't use mana, but it could eat up an ability activation, which means the Hiryu is using less actual abilities overall (thus spending less mana). This is something
@Khaelor and I were looking into a while ago, but it is extremely tedious to test and we moved on to other things.
If you want your Hiryu to bottom out its mana, give it Chiv/AI and it will drop mana just like any other pet.