As HS Registrar, I receive frequent requests for Education verification.  In order to obtain enrollment date, I need to drive to Core > Users/Access > Profile > Edit User Profile Data > Student Enrollment.  Per my conversation with a BB representative, at this time, it isn't possible to add enrollment and graduation dates directly to the contact card without the use of a custom field. Even still, this field would not update automatically so a member of your staff would need to manually enter it in when the student is enrolled. 

I think it would be most helpful to have this information populated as part of the standard fields within the Contact Card.