Mack the Knife
"Mack The Knife" by Bobby Darin was the number 1 hit song on October 22, 1959.
Sherry by The four seasons
(Let me be your) Teddy Bear
Hey Jude-The Beatles
Help followed by Eve of Destruction
Please Mister Postman by The Marvelettes
Sheila by Tommy Roe followed by Sherry-by the Four Seasons
don't be cruel/hound dog-Elvis Presley
The first Billboard number one hit in 1955 was Let Me Go Lover by Joan Webber. However it was really not a rock song
Bon Jovi is a rock and roll band. In addition to the band's extreme success in the rock and roll arena, Bon Jovi became the first rock band ever to have a number one hit on the Billboard Country Chart with 'Who Says You Can't Go Home' in 2006.
The Billboard Rock charts began on January 1, 1955...sorry there is no answer to your question.