Maybe it was because Ash had already learned from Annie how the Grapefruit Island Gym's challenge worked and had prepared himself and come up with a few contingency plans? Or perhaps it was because Ash was already quite strong, and his Pokémon were all willing to fight hard?
In any case!
While Annie was fast asleep at the inn, Ash, Misty, and Tracey safely reached Grapefruit Island, just a few miles from the metropolis, aboard their Lapras. They successfully qualified for the challenge and narrowly defeated the Gym Leader, Yas, a flashy guy who had tried to hit on Misty. Then, before dusk, they returned to the inn in the metropolis with the Spike Shell Badge in hand.
After reuniting with Annie, Ash and the others, who had earned their third badge on Grapefruit Island, immediately resumed their travels in order to collect their fourth badge as soon as possible and enter the Orange League competition.
Along the way, Annie once again split off from the group without a doubt.
For the next two or three days, Ash, Misty, and Tracey didn't run into her at all. Instead, while traveling aboard Lapras, they met a trainer their age named Sayo, who was speeding along in a yacht and nearly hit them.
After they had introduced themselves, the three of them, hoping to travel in greater comfort and having received a sincere invitation from Sayo, didn't think much of it. They all abandoned their poor mode of transportation—Lapras—and accepted his invitation to board his yacht.
After all, he said that, like Ash, he was training in the Orange Islands to compete in the Orange League, and had just earned his third badge on Grapefruit Island. Their routes happened to overlap, so they could travel together and look out for one another.