Twiggy Trees are subject to world regrowth and Grass Geckos have a chance of popping out of transplanted grass tufts, thus allowing you to obtain both variants in a single world, however, there's no such option for berry bushes so you either have one or the other. Maybe you get lucky a couple of the other variant down in the caves but so far in a 200 day juicy berry world I've had no luck finding a single berry bush which is locking me out of the bush hat (And I also really love using normal berry bushes to decorate my gardens).
So I suggest a reliable (or maybe even unreliable heck as long as it's possible) to transform berry bushes into their other variant, perhaps something similar to the Lunar Experiment from Hallowed Nights which is able to turn objects into their lunar equivalents but instead a potion that is able to turn Juicy Berry Bushes into Berry Bushes, Grass Geckos into Grass Tufts and Twiggy Tree Saplings into Saplings.
This would make it so you are able to obtain your preferred variant no matter what world you make after gathering enough resources to get ahold of these potions.