I would avoid putting cereal in the bottle. Most doctors will recommend against it, as it could lead to choking. Just wait until you're given the green light from your pediatrician to begin solids before giving cereal. Most doctors will also prefer that the cereal learn to be eaten from a spoon not a bottle (unless of course your baby has digestive issues such as frequent spit up or reflux).
Our pediatrician gave us this basic guideline - bottles should be no more than the baby's age in months + 3. So, at 3 months the maximum amount she should be drinking per bottle is 6 ounces, with no more than a total of 36 ounces per day. Of course EVERY baby is different with unique nutrition needs. I would consult your pediatrician to ease your mind.
We also noticed a big growth spurt around 12-15 weeks with our baby and he seemed very hungry. She could just be going through a growth spurt and need all the calories and nutrients to support her growing mind and body.