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.
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).