TL;DR: it prefers to target ferrous metal
This is likely a hold-over from earlier editions, which had this text in the 2e Monster Manual entry for Rust Monster:
Rust monsters, being none too bright, stop pursuing a fleeing party for one round to devour metallic items, such as a handful of iron spikes, a mace or a hammer, if the party throws them behind. Rust monsters go after ferrous metals such as iron, steel, and magical steel alloys, such as mithril and adamantite. They choose such metals over valuable metals such as copper, gold, silver, or platinum. In fact, they would continue to pursue a party that just dropped a fistful of copper coins, for example, in hopes of getting the much-preferred ferrous metal of armor and weapons.
In 3rd edition, the Monster Manual has this text:
It prefers ferrous metals (steel or iron) over precious metals (such as gold or silver) but will devour the latter if given the opportunity.
Thus, the action describes a preferred target for the creature, being ferrous metals. It could well be that the ability might also corrode a non-ferrous metal .. but with 5e's "what the rule text says but nothing more" general principle, then it actually wouldn't, RAW.
So, generally, the statement "But seeing as bronze is not ferrous, it cannot be targeted" is erroneous, as it should really read "it won't be targeted".
There are also two "Ecology of the Rust Monster" articles in Dragon Magazine #88 and #346 that go more into the lore. Take what you read there with a pinch of salt, as some text contradicts earlier versions.