As a teacher, there is not a way to connect your existing Google Classroom account to an existing Bloomz class. 

When you connect your Google classroom to Bloomz, this creates a new Bloomz class.

NOTE: If you are wanting to still create a new classroom connected to Google Classroom, then you would need to simply move your parent contacts into the new class. Parents would receive another invitation to join a new class. This would be in the form of an email and/or SMS message and would also be a notification in the app. They would need to accept this invitation to start communicating in the class connected with Google Classroom.

Additional Resources:

• Invite parents from one class to another class/group in bulk