united-states
It is very unlikely that Alice has any cognizable cause of action against Bob.
Before going any further, we should acknowledge that the First Amendment provides similar protections in both civil and criminal court. If something may not be criminalized, then (in most cases) it also may not give rise to civil liability, and vice-versa. So in deciding whether your hypothetical lawsuit would succeed, we can look to both criminal and civil case law.
In order for Bob's words to give rise to civil liability, they must fall under some exception to the First Amendment's free speech clause, or else his words are protected speech and the lawsuit fails.
Advocacy of violence
Let's start with a point of comparison. Imagine that Bob is leading a KKK rally, openly advocating for the murder of people similar to Alice, and the state arrests him and tries to prosecute him for his advocacy of violence. In this example, Bob is Clarence Brandenburg, the state in question is Ohio, and the Supreme Court ruled that Brandenburg's speech was protected by the First Amendment. It based this decision on the fact that Brandenburg's words were neither intended nor likely to cause "imminent, lawless action," and stated that both conditions would be required for the speech to be unprotected. In practice, lower courts have tended to interpret these requirements strictly. Inciting a riot is the sort of thing that might be unprotected, but "mere" hate speech is usually regarded as protected under this test (by modern standards, Brandenburg's words would certainly be considered hateful).
While this is not exactly the same case as you describe, it shows that generalized advocacy of violence is not enough to disqualify speech from constitutional protections. So we cannot simply point to Bob's violent intentions (in either example) as a source of possible liability.
Fighting words
The fighting words doctrine, to the extent that it survives, says that speech may be unprotected if it is so offensive that it provokes a listener to acts of violence. The main problem with fighting words is that the Supreme Court has spent the past several decades steadily narrowing and limiting the scope of the doctrine, most recently in Snyder v. Phelps (2011).
In that case, members of the Westboro Baptist Church picketed the funeral of a US marine, displaying various offensive signs broadly claiming that God kills soldiers because the US is in a state of sin. The family sued for emotional distress, defamation, and invasion of privacy. The Supreme Court ruled that, because the contents of the signs were "of public concern" since they pertained to the US as a whole (and not to the Snyder family individually), the speech was protected and could not give rise to tort liability. Alito's dissent characterized the WBC's actions as fighting words, but the opinion of the court dismissed this in a footnote, citing the lower court and United States v. Stevens, which broadly stands for the notion that the government is not at liberty to invent new categories of unprotected speech whenever it sees fit. Put another way, the footnote was tacitly suggesting that Alito was putting a square peg in a round hole.
While it might appear from the above case that the fighting words doctrine could have been used, if the message had been personal to the Snyders, Wikipedia has a lengthy list of other (modern) cases involving the doctrine, and to make a long story short, almost nothing seems to qualify as fighting words in practice.
True threats
A "true" threat is a statement that causes the listener to reasonably fear an act of violence on the part of the speaker. True threats must be read in context, but can be made recklessly (subjective intent is not required). Since you have given us no contextual information (When did Bob say this prayer? Was there an audience? Would a reasonable person take him literally, or interpret it as a joke or hyperbole? And if it is taken literally, is it more reasonably interpreted as a prayer, or as a veiled threat?), I cannot further analyze this exception. What I will say is that a vague "I pray that you die," apropos of nothing, does not sound like a threat to me, but I do not believe there is case law directly on point. Depending on the circumstances, it might be ruled a question of fact for a jury.
Freedom of religion
But it turns out that freedom of speech is only the first problem with this lawsuit. Bob can (rather credibly) argue that his prayer is an exercise of his religious beliefs. Under the Religious Freedom Restoration Act, that means any tort law purporting to restrict his prayer is automatically subject to (as-applied) strict scrutiny, and the lawsuit probably fails on that basis. Note however that the RFRA is a federal law, and the Supreme Court has ruled that it cannot be used against state laws. Nevertheless, many states have enacted analogous laws, and so this defense might be available in state court.
Even if there is no RFRA-like law available, the lawsuit probably still fails on a freedom of speech basis anyway.
