Figure a basic bird mount would have something like the following:
Flight 3 (Wings; Innate; 16 mph, 250 feet/round; flight speed could vary by a rank or two depending on the specific bird, but 3 is about right) - 2 points
Growth 4 (Permanent; Innate; +4 STR and STA and +1 size category; 4 STR is 400 lbs. carried weight, enough to comfortably carry one Musian man and his equipment, possibly two riders; large size ensures the bird is big enough to accommodate a rider) - 9 points
Stamina 1 (brings STA total to 5 for Toughness and Fortitude caps) - 2 points
Parry 5 - 5 points
Dodge 5 - 5 points
Will 5 - 5 points
So that would be 28 PP to cover all caps and the bare necessities. That means you'd need to spend 6 points in Sidekick, minimum, and you'd have 2 extra points. This doesn't account for any combat training (Advantages) or Skills that the bird would have, nor for other stats the bird probably has naturally, like Agility and Awareness. You'd also get a few points back by reducing its Intellect since it would be animal intelligence. That helps make the cost a little easier to swallow.
I suppose that's not as bad a point-sink as I thought, and I'd rather see a Sidekick bird than a Minion bird. A Musian rider's bird mount is a very close companion. The bird is usually very well-treated, in the same way many cavalry soldiers took very good care of their horses.
Plus, it's a long, long way down and the ground below the highlands is very inhospitable (see the Religion post for more info). So you could go Sidekick route if you'd like.
I'd say something like Expertise: Animal Handling or Expertise: Animal Training, possibly linked to Awareness or Presence rather than Expertise: Riding would be appropriate. Bird-mounted Musian soldiers are usually taught to train the birds as well as ride them, so I would allow for a broader skill than just "Riding." A Musian could also use this skill as a Persuasion skill against other animals, effectively making him something like a D&D Ranger. You won't be able to train another animal as a minion/sidekick (I'd rather players not have personal armies

) but you'd be able to influence any fauna you come across. It can also be used for hunting to an extent -- the idea being that your character's understanding of animal minds allows him to know how to track and hunt animals.
The Expertise: Animal Handling will also help justify your mount gaining new abilities if you buy another rank of Sidekick later in the game.
You could use Expertise: Animal Handling in place of Vehicles for controlling your bird outside of a routine flying situation (i.e., in combat). Most Musian mounts are trained for combat, so the DCs might be lower (I'll have to think about how this can work exactly), but you would definitely have to make a check to do fancy things or do something like make your mount use Extra Effort.
Does that sound reasonable?