Alright man, that's really good that you count your calories. Just remember that if you are looking to build muscle then you get about 1.5-2 times your bodyweight of protein. So if you're 138 pounds, you should be eating about 207 - 276 grams of protein EVERYDAY. Since I assume you are bulking to build muscle, .5-.8 times your bodyweight of fat should be ideal. So 70-110 grams of fat is should be good for you. The rest of your calories should go to carbohydrates. I know that 207-276 grams of protein sounds insane, but you asked for information about bodybuilding and that is what you're going to get. Unless you have the money to purchase lean meats to hit that number of protein everyday without consuming too much fat, I highly suggest that you invest some money in whey protein, since it really helps on reaching that number of protein intake everyday.
Now that you know this information, it DOESN'T matter how you reach those numbers. You can customize your diet however the hell you want to, just make sure you are getting enough carbohydrates in the morning so you have energy to operate correctly, since your carbohydrates has more than likely ran out using all its energy to help the muscles repair itself during your sleeping period. If you want more protein in the morning than at night, then go ahead. It's when you are sleeping that your body will use most of what you have fed it. Your breakfast plan seems pretty good, but like I said it doesn't really matter how you customize your diet just as long as you hit your required protein, fats, and carbohydrate intake consistently. So go ahead and have that breakfast plan just as long as you calculate every other meals to reach your goals.
So to answer your question, what's a good breakfast for bodybuilders? A good breakfast for bodybuilders would contain sufficient amount of carbohydrates to give them the energy they need to operate... other than that it doesn't really matter how many proteins or fats you consume AS LONG as the proper amount is consumed at the end of the day.