They still use it. This time they extend the “Busssssccccchhhh” longer so that the actor is looking around, waiting for it to stop. META!
Ai yi yi yiii
I am the frito bandito
I eat Fritos corn chips I love them I do
I want Fritos corn chips I get them from you
Must have been the second verse. 
We sang parodies in second grade. I’d probably never heard the originals, but I remember the parodies
Winston taste bad like a cigarette had
No filter, no flavor, it tastes like toilet paper
Like the one I just had.
I barely remember women playing tennis and smoking and manly men in cowboy hats on horses smoking in commercials on TV but I do remember part of the Winston jingle because we little girls played a hand clapping game that started with it:
Winston tastes good like a cigarette should
Winston tastes good like a
– Oooh Ahhh I wanna piece of pie
The pie too sweet, I wanna piece of meat
The meat too tough, I wanna ride a bus. . .
I remember TV ads saying you could go to Marlboro country. It looked like a great place! And it had great music! Not quite a jingle like the OP, but I could hum along.
Since my mom smoked Marlboros, I figured if I just stood close to her when she smoked, I could be transported along with her. Like it was some tobacco transporter device.
It’s a wonder I never took up smoking.
Garfield 1, 2-3-2-3 Garfield 1, 2-3-2-3!
“You can take Salem out of the country but
you can’t take the country out of Salem!”
The earliest I personally remember.
I remember singing(to the tune of the Colonel Bogey March):
Comet, it makes your teeth turn green
Comet, it tastes like gasoline
Comet, it makes you vomit
So buy some Comet and vomit today
No idea if there was an actual commercial for Comet using that song. Or why you’d brush your teeth with it.
You could also have ordered the LP:
There apparently have been many other subsequent releases on both cassettes and CDs.
All those beer jingle memories, and no one mentioned the all-time classic Rheingold beer song* (Rheingold sponsored N.Y. Mets games going back to their days in the Polo Grounds)?
Ballantine beer (which sponsored the Yankees) had a jingle too, but since no one in our family could tolerate the Yanks, I don’t remember how it went.
*some years ago on the Dope I started a thread about advertising jingles which featured my fractured memory of how the Rheingold jingle went:
My beer is Rheingold, the dry beer
I drink Rheingold whenever I buy beer
Rheingold’s taste ain’t too sweet
Smells like old stinky feet
Bud and Schlitz can’t compete
with my beer!
I was going to mention this one. I remember it well. It’s based on Emile Waldteufels’ Estudiantina Waltz. I hadn’t been aware of it until I googled it, but he also wrote the instantly familiar Skater’s Waltz.
I had one music teacher who taught one lesson in which he featured classical music that had been used in popular culture, like this and the Lone Ranger’s William Tell Overture.
My beer is Rheingold the dry beer.
Think of Rheingold whenever you buy beer.
It’s not bitter, not sweet, it’s the extra dry treat
Won’t you try extra dry Rheingold beer?
It was a major mystery to me as a kid how beer could be dry. It seemed pretty wet to me!
Tide was designed, with mothers in mind, to get out the dirt kids get into.
You get a lot of dirt with children, you get a lot of clean…with Tide.
Pour it ON, Pour on the Iron City beer.
Slapkling robust flavor, that does your thirst a favor, when your REALLY ready to pour it on,
Pour on the Iron.
Whole version.
Lemon Pledge, very pretty (too long to type)
And just for shits and grins…The Flintstones selling Winston Cigarettes
A couple of folks beat me to my earliest, Pepsodent and Brylcreem. So I offer numbers 3 and 4:
[whistle] Mabel! Black Label!
Carling Black Label Beer!
Drive in to McDonald’s,
Drive in to McDonald’s,
For forty five cents you get a three-course meal.
Drive in to McDonald’s,
Drive in to McDonald’s,
Forty five cents at McDonald’s.
It’s all over town!
Burger, milkshake, french fries.
Mom used to sing a radio jingle she remembered from the '40s which would crack me up as a kid:
If Nature should forget
Go to your medicine cabinet,
Get Ex Lax, Ex Lax,
if, If, IF . . .
Let’s all go to the Dairy Queen,
I see one just down the street!
We’re all going to the Dairy Queen
to get a fresh, frozen treat!
God, there are some memories here–I guess i am getting old in that I can still sing 9or at least hum) a whole lot of them.
Two more: I think this was the 1960’s, but who doesn’t know the line: “There is nothing so clean as my Burger Machine.” McDonalds Television Ad - c. 1970's - YouTube
I think the oldest one was Diana Shore singing “See the USA in your Chevrolet” back in the 1950’s–Dinah Shore "See the USA in your Chevrolet" - 1953 - YouTube
Come to the Florida Sunshine Tree
for fresh-tasting orange juice nat-tur-al-ly!
Orange juice with natural vitamin C,
from the Florida Sunshine Tree!
It’s the Radial Age,
now the world is safer
on a great new tire!
It’s the Radial Age,
BF Goodrich boosts your mileage
so much higher!
New tire from B-F-G,
the Radial 990!
One ride and you will see
it rolls like nothing that you used to know!
It’s the Radial Age,
It’s the Radial Age!
Escape, come over
to Royal Crown Cola!
It’s the mad, mad,
mad, mad cola!
RC, the one with the mad, mad taste!
Let us shake the cola drag,
check the one that’s really mag!
It’s the mad, mad,
mad,mad cola!
RC, the one with the mad, mad taste!
RC!
“Marine’s Hymn” is the odd one there. Its meter (syllables in the lines) is 8.7.8.7, the others are meter 7.6.7.6.
My post (there may be errors in it) on that subject from one of several earlier threads: https://boards.straightdope.com/sdmb/showthread.php?p=12979636#post12979636
The best part of that commercial was Joey Heatherton! 
‘I like Aeroplane Jelly,
Aeroplane jelly for me’ … etc
Australia’s favourite flavoured, sugared gelatine crystal mix has used the same song since the 1930s. The version thats broadcast now is from the 1940s, and pretty well embedded in the reptile sector of the brain of anyone who’s listened to Australian commercial radio since Rommel.
My own prehistoric memories of jingles involve Ron Hodgson a used car dealer whos adverts benefited from jaunty songs and the occasional bit of sped-up Benny Hill style camera work. Lovely stuff, as Alan Partridge would agree.