In Lessing's "Through the Tunnel," the bay is and represents something the boy isn't supposed to do or can't do; it is something the older boys can do, and the boy wants to do. The bay is basically a rite of passage. Or, more specifically, swimming through the tunnel in the bay is all of the above.
Notice that once he's done it, once he's accomplished his goal, he is in no hurry to go back. He's done it, he's made it, he's proved himself, he's matured. He's proven he belongs.
He begins the story as a little boy who seeks attention in any way possible, and desperately needs the approval of others. He matures and in the close of the story he is content in what he's done and in who he is.
For Jerry, the wild bay seems to represent adulthood and maturity. He's a young adolescent, and so it seems natural that he no longer wants to accompany his mother to their usual, "safe beach," the beach they've always gone to in the past. Instead, he prefers to go to the "wild bay" where the older boys, who are like "men to Jerry," hang out.
At the wild bay, Jerry sees, "small promontories and inlets of rough, sharp rock, and the crisping, lapping surface showed stains of purple and darker blue." This place sounds dangerous, painful, and even unpredictable. The "stains" of dark blue and purple might remind us of bruises, and Jerry runs, "sliding and scraping down" to the water (more words with painful, damaging connotations). The wild bay lacks the safety of the beach where Jerry used to accompany his mother. When he looks back at her there, he sees her as a "speck of yellow under an umbrella that looked like a slice of orange peel." Such beachy, sunny colors and vacation-appropriate citrus fruit references correlate with the safety and sunniness of childhood; juxtaposed with this description, the wild bay feels colder and lonelier to Jerry, but he wants to remain there nonetheless. Independence (and the maturity from which it comes) can be lonely.