At this stage your baby holds the bottle on her own, this is a big step in her life. It can be considered as a milestone. It gives you a feeling of achievement and makes you feel proud as it is a sign that she is not only growing but also her motor skills are developing. Sometimes your baby needs little encouragement and guidance as to how to hold her own bottle.
At this point try to make your baby get used to the movement. If you are feeding with formula, your baby can hold the bottle at 4 months. Take her hands and gently press against the side of the bottle. This will make your sweetie pie get the feel of the bottle and help her understand the correct arm motion. But you need to still keep the firm grasp of the bottle as she is still too young to support the weight of the bottle by her own.
Only once your little princess is between 6-10 months old you should allow her to hold the bottle along with you. Once you feel she can support the weight by herself you can experiment by letting go of the bottle for short periods. Best way to make her practice to give her empty bottle at times. Best time to practice is to give her the bottle filled with formula during the first feed of the morning, when is she the hungriest. Avoid distractions while teaching her how to hold her own bottle as babies are too sensitive. Turn of bright lights, music and keep the toys away before you start feeding. She needs to concentrate on learning to hold the bottle and learn the new motor skill.
Remember all the babies develop differently and not all the babies start holding the bottle at the age of 6 months or soime. If your baby won't hold the bottle, give her some more time. So you can always guide you little princess to understand the relationship between the feed and holding the bottle. At she will understand and start holding the bottle on her own.