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, and is a result of the Bill of Rights being "incorporated" to apply to state and local governments via the 14th Amendment due process clause, rather than the original U.S. Constitution's or the 14th Amendment's privileges and immunities clause which apply only to U.S. citizens.
Foreigners also have a right under U.S. treaties to consular assistance, 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.
One of the leading cases addressing all of these issues is Sanchez-Llamas v. Oregon, 548 U.S. 331 (2006). In this case, the U.S. Supreme Court held (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)