Here is the relevant excerpt:
In all cases affecting ambassadors, other public ministers and consuls, and those in which a state shall be party, the Supreme Court shall have original jurisdiction. In all the other cases before mentioned, the Supreme Court shall have appellate jurisdiction, both as to law and fact, with such exceptions, and under such regulations as the Congress shall make.The key part here is that since the state of Arizona is a party in a case, the Supreme Court shall have original jurisdiction. This means that Judge Bolton does not have judicial authority to rule on any aspect of SB 1070.
h/t to Lynn Woolley Show
UPDATE: looks like THIS may be the original source of the aforementioned claims.