Someone can correct me if I'm wrong since this info is off the top of my head.
You need 90 bushido in order to receive a lesser hiryu from say a tamer.
At 120 bushido you can control a lesser hiryu with 95% success...somewhere around that anyways.
And from what I recall you need GM bushido in order to bond your lesser hiryu. Someone else can confirm the skill since I already had higher than 110 when I had bonded mine.
In terms of a published formula, there is not one to my recollection.