Sayyed-hood is passed down from Father to Son. For the Bab to be a Sayyed, all of his forefathers must also be Sayyeds but none of his forefathers (4 generations up) were Sayyeds.
This is the Bab's genealogy:
|Click to enlarge|
published in Shoghi's "The Dawn-breakers":
On the far right these have been mentioned as the Bab's forefathers: Mirza Nasrullah, Mirza Ibrahim, Mirza Abu'l-Fath, Mirza Muhamad Rida.
As you can see, according to Baha'i history books, the Bab's forefathers were all "Mirza" and the claim that the Bab is a "Sayyed" is a lie made up by Baha'is and followers of the Bab.
|Wikipedia page of Bab says that "He claimed to be a Sayyid"|