I believe that I have figured out how to get an iPhone, iPad or iPod Touch to autocorrect with a bluetooth keyboard connected.
First, make sure that you have QuickNav turned off.
If you are not sure how to do this, just press the right and left arrows together on your keyboard.
Then, try this:
When VoiceOver tells you a word is misspelled, hit the Backspace key once.
Now a suggestions list pops up, but I doubt VoiceOver will tell you that it has.
Hold VO keys on your bluetooth keyboard (Control and Option) and navigate to the right.
Eventually, you will get to the list of suggestions. When you find the one you want, just press VO Space bar on it.
Voila! You have successfully used autocorrect.