I wonder if there's some secret key combination that would do it. The reason I say that: it looks to me like Logitech's new Ultrathin Keyboard Cover for iPad Mini has a microphone key (not found on Logitech's other keyboards as far as I can tell). I assume it must be for dictation. What Bluetooth key signal is it sending? If it's sending some key combination, maybe that could be tested by connecting it to a Mac or PC instead of an iPad.
Anyway, I'd like the same thing--and there's at least some small cause for hope.
Haven't heard of that combination, but I know if you have an Eject key it will do that. And some keyboards even have a key with a little keyboard icon, for "show onscreen keyboard."
However, that's awkward and takes away some of the convenience of dictation: hit a key combination, then tap something on the screen, then tap again, then hit the keys again? It's good to have a solution, but I sill hope for a better one!
And now I've seen a second keyboard with a mic key: Belkin's FastFit keyboard (similar to the Logitech). I see a mic key on the FULL iPad version, not on the Mini version.
Both companies (Logitech and Belkin) are showing images of a product that is not available for sale quite yet--soon, they say. So, I'll believe this mic key when I see it in reviewers hands.
But if it IS a real key on some Bluetooth keyboards, then there may be some keyboard shortcut associated with it. (Like ctrl-option-shift 7 or something you'd never find by trial and error?) That would allow you and I to avoid tapping the screen every time (and avoid blocking half the screen with a needless 2nd keyboard during dictation).