If you go to the USCG
documentation center website, on the left is a category called FAQ. Click it and one of the questions it addresses is what is required with an
ownership change. It seems they need a new application, payment of
fees, and additional documentation (I assume a copy of the bill of
sale that substantially comports with their model bill of sale). So I think your application is incomplete at this point.
In addition, if your state requires it, you will need to register the vessel. If you complete the USCG documentation they will send you a confirmation
email that everything is received and they are processing your application. Print out that
email and take it with you when you go to register. You usually don't have very long to get this done so definitely make haste to get her all
legal.
If you have questions about what USCG needs to complete your application, just call them. They are very helpful, if a bit snippy sometimes.