You can try to get it from $bean->email1 which is a proxy field providing the primary email, but it’s not always filled, and it’s not always what you want.
The real solution is to navigate the email_addr_bean_rel relationship and work with the list of related email_addresses.
Here is a sample bit of SQL that might help you understand the relationship:
SELECT ea.email_address
FROM email_addresses ea
LEFT JOIN email_addr_bean_rel ear
ON ea.id = ear.email_address_id
WHERE ear.bean_module = 'Contacts'
AND ear.bean_id = 'ed6b0688-54bf-3769-bc06-5ad0aab95e73'
AND ear.deleted = 0
AND ea.invalid_email = 0
ORDER BY ear.primary_address DESC LIMIT 0,1
But you don’t have to use SQL, you can use beans and navigate the relationship. Something similar to this post, without deleting the emails, of course.