The Bull Arab diet will need to include animal proteins, healthy carbs, vitamins, minerals, and omega fatty acids--nutrients every dog needs to maintain its health in the long term. This means the best dog food for Bull Arabs is premium dry kibble, as it contains balanced portions of the above-listed ingredients.
These hybrids will do best with premium food that's formulated for active breeds. SportMix and Dr. Tim's are recommended brands that carry excellent lines of high-energy premium food.
Adult BAs, depending on their age, size, metabolism, and activity levels, will need about four cups of dry food per day, divided into two meals. BA puppies will need a bit less: again depending on age, about 2¾ cups per day, divided into three meals (not two) until seven months of age.
For more info on feeding a Bull Arab from puppyhood through maturity, see this Bull Arab feeding guide:
Dog AgeDog WeightFood TypeAmountFrequency2 Months15 lbsDry (Puppy formula)0.5 cups3x/day4 Months25 lbsDry0.75 cups3x/day7 Months50 lbsDry1 cup3x/day10 Months60 lbsDry* (Puppy/Adult)1.6 cups2x/day12 Months70 lbsDry (Adult formula)1.75 cups2x/day14 Months+80 lbsDry2 cups2x/day*--Around this time, transition to adult food by mixing in adult formula with the puppy formula, in slowly increasing amounts with each meal, for one week.
Try if possible to stick to the above-listed portions. If constantly overfed (and under-exercised), these hybrids can become overweight--and a fat Bull Arab will have numerous health problems and a potentially shortened lifespan. You can help control your BA's weight by having consistent feeding and exercise schedules, by not feeding the dog table scraps, and by not leaving food in the dog's bowl all the time.
If you're worried your Bull Arab is overweight, try this test: run a hand along the dog's side, and if you can't feel any ribs, it's diet time--which means less food and more exercise!