No, Doc Holliday did not ride with Billy the Kid. While both are famous figures of the American Old West, their paths did not cross in a significant way.
Doc Holliday was a gambler, dentist, and gunfighter known primarily for his association with Wyatt Earp during the gunfight at the O.K. Corral in Tombstone, Arizona. He was active during the late 19th century, particularly in the 1870s and 1880s.
Billy the Kid, on the other hand, was a notorious outlaw and gunfighter who became famous for his role in the Lincoln County War in New Mexico during the same era. He was active primarily in the early to mid-1880s.
While both men were involved in the lawless environment of the American West, they operated in different regions and associated with different groups of people. There are no historical records or evidence to suggest they rode together or had any direct interactions.
In summary, although both Doc Holliday and Billy the Kid are legendary figures of the Wild West, they belonged to separate stories and timelines, and there is no documentation to indicate that they ever teamed up or traveled together.