While Dragon Ball's iconic protagonist has always had a deep friendly streak that has turned even some of his most obsessive rivals into strong friends and allies, the friendship that kicked off the entire franchise was with the genius inventor Bulma. First meeting when Goku was just eleven and Bulma was only a teenager, the pair's dynamic started off on the wrong foot, leading to an epic misunderstanding before they joined up to scour the world for the mythical Dragon Balls and summon the Eternal Dragon for a magical wish. With Goku and Bulma's friendship continuing to endure all their lives, through the current anime/manga series Dragon Ball Super, here's how their dynamic has evolved over the years and what's remained the same.
At first, Goku and Bulma's friendship was one of convenience: Goku refused to give up his four-star Dragon Ball, as it was his late grandfather's parting gift to him, leading him to agree to accompany Bulma as the duo search for the other six Dragon Balls. By the end of their journey, which included the introduction of several longtime Dragon Ball characters like Master Roshi and Bulma's eventual boyfriend Yamcha, a genuine friendship between the two had blossomed, which carried on throughout the overarching Dragon Ball story.
With Goku raised in relative seclusion at Mount Paozu, he was deeply naive about the ways of the world. Bulma constantly grows frustrated with him for his immense amount of ignorance, often played for comedic effect while their friendship endures and grows.
While Goku and Bulma would stay friends, Goku often secluded himself from her and his other friends for years at a time, training for the next major martial arts challenge or tournament. At the start of Dragon Ball Z, Bulma had presumably not seen Goku for the five years since the end of the original Dragon Ball series, and was surprised when he revealed that he and Chi Chi had a young son named Gohan. Bulma was also deeply affected when Goku was killed in the fight with his evil older brother Raditz, and pondered while searching for the Dragon Balls on Namek after Goku's resurrection whether she would have been better off romantically pursuing Goku rather than Yamcha (before ultimately dismissing the idea entirely).
Just as parenthood hadn't changed Goku and Bulma's dynamic all that much, Bulma having her own son, Trunks, with Vegeta, did not significantly impact her friendship with Goku either. However, while Bulma still grew comically frustrated with Goku at times, it was clear that the wisdom of age and experience led to their friendship becoming much more profound, with Bulma able to confide and trust in Goku on a level that she hadn't when they were both children. This could be seen when Goku and Piccolo prepared Trunks and Goku's second son Goten to learn the Fusion Dance and become Earth's last, best hope against Majin Buu, with Goku assuring Bulma that everything would be alright and her son would come out okay.
Throughout Dragon Ball Super, Goku, Bulma and their respective families spend considerably more time together than they did during DBZ, largely because Goku and Vegeta's dynamic has significantly improved. This means more times that Bulma has gotten annoyed at Goku, often when the absent-minded Super Saiyan asks his old friend for money for a variety of reasons throughout the series. While Bulma does often pay up, she's also visibly frustrated by the promises Goku makes on her behalf without her agreement. Still, at the end of the day, Goku and Bulma's friendship is just as strong as it was when they first met decades ago on Mount Paozu.