If the 9th overturns Bolton, it goes back to her court. Right?
Yes, but only to implement the order described by the 9th Circuit. That order can be just about anything, from "find more facts, then decide again," to "remove the injunction, period."
And keep in mind that the only thing before the 9th is the preliminary injunction enjoining Arizona from enforcing the mandatory effect of the law. The governor can, of course, make it an executive policy for the law enforcement to inquire about the immigration status for 100% of the people it develops reasonable suspicion of. In other words, she can implement by "executive order," rather than by legislation.
Doing so would produce additional facts that could undermine the grounds for much (if not all) of Bolton's decision. For example, ICE does not become overloaded with requests; legal aliens aren't unreasonably detained, etc.
It's hard to keep track of the full game -- news reports tend to isolate attention to small facets, and often to irrelevant facets.