In the United States Bob would have a protected right, under the US Federal First Amendment, to discuss his case publicly, give his side of the matter, and speculate on things he does not know for certain.
The court can order that particular documents be kept confidential or "under seal". But unless it makes a specific order to this effect, Bob is free to reproduce them if he so chooses.
The court can order the parties, and non-parties such as newspapers, to refrain for publishing accounts of the case, ot to restrict such accounts in various ways, if there is reason to believe that otherwise a jury might be biased and a fair trail impossible. But such orders must be limited to the degree of restriction required for such a purpose. Such orders have been challenged in the past, in several cases by the press, and higher courts have overturned them when they were judged too broad. In any case the court must make a specific order (sometimes informally called a "gag order"). No such rule is in place by default in the absence of a specific order. If fairness can be preserved by locating the trial in a different area, or by careful jury selection, the court must generally do that rather than restrict speech.
Bob would be liable if he committed defamation on such a blog. If Bob makes statements of fact that are false, and that damage the reputation of someone, that person may be able to sue for defamation. Depending on the circumstances, such a suit might have to include evidence that Bob knew the statements were false, or that Bob was recklessly indifferent to their truth. This i9s known in US law as "actual malice".
Note the accurately reporting the content of court proceedings, even if people make allegedly false statements in testimony or to the court, is not defamation.