Bob is a non-US citizen and is visiting the USA on a tourist visa. . . .
Can Bob invoke the 5th amendment to avoid self-incrimination?
Yes.
The 5th Amendment is a right applicable to all criminal defendants or potential criminal defendants, not only to U.S. citizens. (It might not apply, however, to certain foreign diplomats who are immune to criminal prosecutions in the U.S., since they cannot "self-incriminate" in the sense of making themselves subject to a U.S. criminal prosecution based upon the information that they disclose.)
This is directly true in federal cases as a result of the 5th Amendment to the U.S. Constitution (and originally this applied only to federal court cases). In state and local courts in the U.s., this is true as a result of the 5th Amendment to the Bill of Rights being "incorporated" to apply to state and local governments via the 14th Amendment due process clause of Section 1 of that amendment, rather than the original U.S. Constitution's or the 14th Amendment's privileges and immunities clause which apply only to U.S. citizens.
The decision to use the 14th Amendment due process clause rather than the 14th Amendment privileges and immunities clause, was made, in part, because the Slaughter House cases, decided by the U.S. Supreme Court in 1874 before the incorporation doctrine had been developed, has narrowly interpreted the privileges and immunities clause.
U.S. Supreme Court Justice Clarence Thomas in a dissent in the case Saenz v. Roe (1999), has [argued][4[] that this was a mistake and that the Bill of Rights should instead have been incorporated via the privileges and immunities clause of the 14th Amendment, which if done would deny non-U.S. citizens in the United States the protections of the U.S. Bill of Rights in state and local courts.
The 5th Amendment to the U.S. Constitution states (with the pertinent language in bold):
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a grand jury, except in cases arising in the land or naval forces, or in the militia, when in actual service in time of war or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
Section 1 of the 14th Amendment to the U.S. Constitution states (with the pertinent language in bold and the 14th Amendment privileges and immunities clause in italics):
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
Article IV, Section 2 of the U.S. Constitution states (with the privileges and immunities clause in italics and the repealed third clause of the section related to fugitive slaves omitted):
The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.
A Person charged in any State with Treason, Felony, or other Crime, who shall flee from Justice, and be found in another State, shall on Demand of the executive Authority of the State from which he fled, be delivered up, to be removed to the State having Jurisdiction of the Crime.
Foreigners also have a right under U.S. treaties to consular assistance, under Section 36 of the Vienna Convention, but unlike the 5th Amendment right, this right arising under U.S. treaties has only rarely been afforded an exclusionary rule type protection to foreign criminal defendants if it is denied in the way that 5th and 6th Amendment violations of the rights are foreign criminal defendants are protected. In denying that effect, the U.S. Supreme Court concluded in Sanchez-Llamas v. Oregon, 548 U.S. 331 (2006), which addressed all of these issues, that since most Vienna Convention members to not provide an exclusionary rule remedy (something unique to U.S. law) to violations of this treaty right, that U.S. states were also not compelled to do so.
As applicable to this question, in Sanchez-Llamas, the U.S. Supreme Court confirmed U.S. Supreme Court precedents in place since 1896 holding (among other things) that:
A foreign national detained on suspicion of crime, like anyone else in our country, enjoys under our system the protections of the Due Process Clause. Among other things, he is entitled to an attorney, and is protected against compelled self-incrimination. See Wong Wing v. United States, 163 U. S. 228, 238 (1896) ("[A]ll persons within the territory of the United States are entitled to the protection guaranteed by" the Fifth and Sixth Amendments).
Sanchez-Llamas v. Oregon, 548 U.S. 331, 350 (2006).