I can't speak as to whether it's a bad thing for your Hops roots or not but if you're looking for a way to kill off the ants without the use of poison and you're not in a rush to have them dead you can use the exchange method which I've found to be very effective.
You simply need a shovel and you get a scoop from another ant hill elsewhere and add it to the hill you want to kill (Generally I'm trying to kill both hills so I would exchange shovel fulls between the). The fire ants will kill each other as they're pretty much guaranteed to fight it out if they're from different hills. Once the queen is killed the bed will usually be abandoned (and from best I can tell die completely over a relatively short period of time).
I've lived in the deep Southeast for a couple decades and between that method and sometimes throwing a bit of poison out we've almost never had issues with them.
