How do I transition my baby from using baby sign language to talking?

There is really no transition needed.  This process usually happens naturally.  The more the child begins to speak the less they tend to rely on the signing.  Very few babies will talk and sign at the same time for any length of time.  Most babies will realize that words are words and signs are signs.  Some may use words and signs at the same time for a little while but generally the signs will begin to drop off.  This is also usually a result of the parents.  Parents often slow their signing once the child begins to speak, there is not the huge need to continue when the child can easily pick up words.
However, I highly encourage parents to continue to sign with their child.  It is a great tool that you can use even with older children.  At the very least I would encourage parents to teach their child the ASL alphabet and begin to teach reading using the ASL alphabet.  When you do this you are using all three teaching modes that teachers are encouraged to use with their students (the VAK method of teaching, visual, auditory, kinesthetic).  Signing with children covers all learners in the VAK system.  Signing is visual because they can see the letter being made.  It is auditory because they can hear you saying the letter/word.  And it is kinesthetic because they can make the letter/word themselves.  We take in language as a sound on the left side of our brains and we take in sign language as an image on the right side of our brains.  By using sign language you are working both sides of the brain.  Not to mention that sign language is the third most used language in the United States and the fourth most used in all of North America.  How could continuing to learn a useful language be bad!