"When I got old enough to remember what was going on, I thought everybody was into music," says 27-year-old Billy Burnette in his slow and graceful hint of a Southern drawl. "I thought everybody had an old man that sang and wrote and had records on the radio. I thought it was the natural thing."

The son could be forgiven his misconception. Dad was Dorsey Burnette, the slap-bassman of the legendary rockabilly Rock and Roll Trio (with Billy's uncle Johnny on guitar). During 1956, the group's one year together, they recorded 21 songs, serveal of which ("Honey Hush," "Tear it Up" and "Train Kept A-Rollin'") became milestones of the rock revolution. The Burnettes later moved to the West Coast and more financially rewarding careers as songwriters for Rick Nelson and others.

Dorsey Burnette died last year, but he'd already seen his son achieve success in the music field as a Nashville songwriter with hits like "What's a Little Love Between Friends," "Dance Me Down Easy" and "Are We Dreamin' the Same Dream?" In another year he would have watched in wonder as major record companies engaged in a bidding war for the rockabilly-tinged music of his only son.

"Me and my dad were best friends," Billy Burnette said on a recent Washington stopover (he returns to the Bayou tonight). "I worked for him whenever I could, put together a [pick-up] band and went with him on the road." The original Trio ("I was way too young to realize their impact") made its grab for the ring at about the same time a 21-year-old truck driver named Presley was first going into Sun Studios in another part of Memphis.

Rockabilly, which has been widely revived in recent years (particularly in England) "wasn't a big hit" when his father's trio played it, Burnette says. "They did some touring, but didn't make any money off it. So they said, 'Let's try something else.' They moved to Los Angeles and sat on Rick Nelson's doorstep till they sold him some of their songs."

Billy Burnette and his 27-year-old cousin Ricky (Uncle Johnny's son, who had a hit this year with "Toein' the Line") grew up in and around the studios of California. Billy cut his first single, "Hey Daddy"/"Santa's Coffee" when he was 7, backed by Rick Nelson's band: "To tell the truth, I don't even remember my first record," he says. And then there was Brenda Lee's 16th birthday party, where the youngster formed an impromptu quartet with Nelson, Sam Cooke and Fabian to sing "He's Got the Whole World in His Hands." Which might have seemed a good description of Col. Tom Parker, Elvis Presley's manager, who happened to be at the party. "I didn't know what was happening, didn't know who the Colonel was. He took me on his lap -- there's a picture of it in some teen magazine -- and said, 'Boy, some day you'll do all right!'"

Burnette's other early singles included "Just Because We're Young" (produced by Herb Alpert and written by Dr. Seuss) at age 11 and "The Frog Prince" at age 14.

Within weeks of graduating from high school, Billy had moved to Memphis (with his father's blessings) to apprentice as a studio musician and songwriter with producer Chips Moman (Aretha Franklin, Presley, B.J. Thomas). Eventually he ended up in Nashville, concentrating on songwriting. His first three albums tended to pop-country, though he started to show his rock roots on a pair of 1979 albums for Polydor. From time to time, Burnette would go out on the road, supporting acts like Roger Miller or Delaney Bramlett, but more often he backed his father. One of the bands he put together featured a hot young drummer named Teddy Jack Eddy -- who changed his handle to a more manageable Gary Busey when he moved into films. Those bands would always do some rockabilly tunes, though "I thought that stuff had already been done. I didn't know it would ever be accepted again."

In fact, rockabilly was dormant for many years. Even the senior Burnettes had pretty much forgotten it. "But a lot of it never left," insists Billy, "that feel they had for music. When my dad went on to do his country records, you could still hear a taste of that [rockabilly] sound in there somewhere. People looked for it a bit on my earlier records," but those albums were "way off from it."

Over the past decade, Burnette has made a comfortable living in Los Angeles as a songwriter who's been covered by artists like Conway Twitty, Loretta Lynn, Glenn Campbell, Charlie Rich and Johnny Duncan.

"After I wrote my first song, I decided that was it, I was going to stick with it.I've been having so much fun doing it, but up to now, it's all been an education. My writing's at its peak now," he feels. "I wasn't paying close attention until one day I opened up the trades and started counting." A few weeks ago, six songs he had written were on the pop charts.

It was only in the last two years that Billy decided to develop his credibility as a rock'n' roller. Now that his Columbia debut released this fall, "Billy Burnette," has done well, the singer admits that the legacy of his father's trio "is a lot heavier than I thought it was. I remember when my dad would close his show with "Tear It Up," he'd rock the hell out of it. I will always put one of their songs in my set, my dad's especially. I'm not trying to live off [the family reputation], 'cause there's not a whole lot of people around today who know who they are.

"My mom's in seventh heaven, watching mine and Rocky's careers. I was aiming to please Dad. I wanted him to really think I was doing something. I wish he was around to see it. I think he knew he'd gotten me off on the right track. I feel like the $3-million pitcher for the Dodgers. I just hope I can deliver the pitch for them."