You can start with the ride skill, PHB, p80
RIDE (DEX)
You can ride a mount, be it a horse, riding dog, griffon, dragon, or
some other kind of creature suited for riding. If you attempt to ride a
creature that is ill suited as a mount (such as most bipedal creatures),
you take a –5 penalty on your Ride checks.
Arms & Equipment has some stuff in it too, too much to repost here.
A&E, p91 - Humanoid-Shaped Mounts (Girallon, Gray Render, Ogre) - doesn't have much that helps in the rules area, but does establish that riding a humanoid is possible (at least in 3.0)
Hmmm....reading it again, the section on mounts doesn't seem to be very helpful at all.
Looking back at the Ride Skill
Guide With Knees - ignore this, as the "mount" will direct himself
Stay In Saddle - keep this and add the -5 penalty for ill-suited mount
Fight With Warhorse - ignore, as there is no need to direct your mount - both the mount and rider get their attacks
Cover - allow
Soft Fall - Allow and add the -5 penalty for ill-suited mount
Leap - Disallow. The mount will decide when to jump and when not to
Spur Mount - Disallow. Otherwise, people will start using this just to get more speed
Control Mount In Battle - disallow - the mount decides what she will and will not do
Fast Mount or Dismount - allow and add the -5 penalty for ill-suited mount
Special: -5 penalty for riding bareback - Allow
As for initiative - I would make both roll as normal. The high roll can volunteerilary lower his initiative to go on the same turn as the lower roll, if she so decides.
Good luck!