The White House will delay publication for former national security adviser John Bolton's book for as along as they possibly can, in what is called "prepublication review." The Just Security blog has an explainer of how the process works, and their belief that the current system the government uses is unconstitutional. It also wouldn't prevent Bolton from speaking out publicly about what he knows about Trump's Ukraine extortion now.
As far as Bolton's book goes, the government could keep the manuscript from publication for as long as it wants, essentially. There's existing precedent that suggests the administration could wait until after the election in November; one former Department of Defense employee had to wait 8 months for the process to finish and another former CIA employee waited 11 months. Bolton and his lawyer assert that there is nothing that should be considered classified in the book, and while Bolton is a right-wing kook, he does know this stuff. While the White House says it thinks there is definitely classified information disclosed in it (like this White House has anyone who reads in it), there are other standards ("vague and overbroad" standards according to Just Security) by which it's being reviewed. So with the book in limbo, what can Bolton do? He can go on television and say what he knows.
There is "nothing—no law, no regulation, no nondisclosure agreement—that prevents John Bolton from going on camera today and telling us what he knows," says Susan Hennessey, who is a former intelligence community attorney and executive editor of Lawfare. If he fears for the nation under Trump, there's not anything stopping him other than the ire of Trump and his minions.
There's an outside, very outside, chance that four Republican senators will do their duty and ask to hear from him directly. There's an even slimmer chance that Chief Justice John Roberts would direct his testimony. But the most sure way for Bolton to get his story out is to just do it, and the sooner the better.