Billy Mailman's answer is rather complete, but just simplifying things, the following worked well for me:

If you are playing on a computer:

1. Open the console
2. Right click on Serana OR type "prid 02002b74" and hit enter to select Serana
3. Type "Setpqv DLC1NPCMentalModel Lockedin_var False"
4. Hit enter key

This will cause the "Follow me" dialogue option to reappear.

This solution was found on this link.

Billy Mailman's answer is rather complete, but just simplifying things, the following worked well for me:

If you are playing on a computer:

1. Open the console
2. Right click on Serana OR type prid 02002b74 and hit enter to select Serana
3. Type Setpqv DLC1NPCMentalModel Lockedin_var False
4. Hit enter key

This will cause the "Follow me" dialogue option to reappear.

This solution was found on this link.