There are likely a couple of reasons that Hamlet keeps the conversation confidential.
First, the conversation is a private one between father and son. In the first line of act 1, scene 5, Hamlet is reacting to being led away by the ghost: "Where wilt thou lead me? Speak, I'll go no further." The ghost clearly intends to share his information with Hamlet alone, and Hamlet, considering this could indeed be the ghost of his father, wishes to respectfully maintain that sense of familial privacy.
Second, Hamlet likely feels that the revenge is his alone to bear. He understands the risks inherent in regicide, and he likely wants to spare his closest friends the hazard of being too close to his plans. The less they know, the safer they will be.
And finally, Hamlet likely wants a bit of time to process all he's been told without trying to also explain it to other people. Is this the ghost of his father? Did his uncle really murder his father? Is his mother somehow implicated in the scheming plans of Claudius? The ghost has given him a great deal of information at once, and Hamlet likely needs some time to process all he's heard before sharing with even his closest allies. And, of course, that brings up one more point that would lead to Hamlet's hesitation. If he can't trust his uncle and possibly can't trust his mother, Hamlet is presumably reevaluating those in his innermost circles as he reconsiders the trustworthiness of his allies.
Hamlet swears to his friends that he doesn't mean to offend them, but he believes the ghost is "honest" and that his friends should "O'ermaster't as [they] may," meaning they simply should avoid asking for further details about the conversation.