Well, some golden items can't be fused with mithril. But, the Arcane Ring is not one of those, so you should be able to fuse it. Try doing it again, maybe it was just a one time issue?
So, you have Mithril, but it's just not selectable in the fuse menu? That's bizarre. Well, you might've just missed it, but otherwise that's definitely a bug. No clue you'd go about fixing that, sorry.
If you just got the Mithril, my best suggestion is to load a save before you got the mithril, if possible, and see if getting it again fixes the issue. If not, you might try getting another mithril, and seeing if having a second one "updates" it somehow and lets you see it?