Actually...
Hold on this just a bit. I think it bears some time to mechanically verify what does and doesn't happen. There's varying (and inconsistent) information on this very issue on the Internet, which I discovered this morning looking for some good source material for wording and such.
My apologies if I am confusing matters. It has always been my understanding that Arcane Archer abilities do not stack with unlimited ammunition bows, or more specifically, that they require physical ammunition to work properly. I am confident this is the case for things like Imbue Arrow, but there is ambiguous information regarding Enchant Arrow.
For the record, however, you did not "waste" anything. At the rate that Arcane Archers sometimes go through arrows, having a backup bow that does not consume ammunition is a very handy thing.