I have a few shinies that I thought I'd turn into a Subway Team.....I KNOW they're not the best, but they're shiny dammit! So no, can't change the natures.
They're also 100% pure and completely un-EVed.....not sure their IVs, though, or what their element is for....it's Secret Power, right?
I REALLY don't know much about competitive teams....I normally just pick Pokemon I like, use the first one I find, and go with it through the games....this is essentially the same thing, just with shinies.
This may be relevant....the Bidoof is still in Gen IV.....if that makes any difference.
Any opinions you're willing to give would be VERY appreciated.