I am looking for ways to transport my golf club set in a scooter. I don't own a car because I live in a continuously traffic city.
I am looking for the best way to transport my golf club set to enjoy this sport
Many years ago, I've just laid a golf bag with a cover over the club heads crosswise on a motorcycle luggage rack, strapped it on with bungee cords, and ridden to the course. If you have a full size motorcycle (probably 175 cc or larger with a conventional style frame/saddle/bars, not a scooter shell) this is likely to be viable if you have a rack.
Lacking a rack, you might be able to strap a fully enclosed bag lengthwise on the passenger seat. It wont' be as secure, but if you drive slowly, it'll stay on.
If you're willing to build something, a vertical basket beside the back wheel on one side or the other is the way to go. A covered golf bag is still recommended, but not absolutely required, as gravity will keep the clubs in place.