I have a "workshop microwave" (don't try this with the one in your kitchen :no and have had success the 3 times I've tried it.Microwave drying can work, but you need to be careful. Only heat for short periods of time, as in a few seconds. Then let rest for e.g., a minute and repeat.
Here's how I would do a rough-turned bowl (say 9" diameter, about 1" thick walls.)
First, I weigh the piece. (Digital scale from Harbor Freight, in the region of $12 on sale.)
Then blast it for 90 seconds -- leaning backwards some, open the door of the microwave to let the steam out.
Take the piece out, weigh it. Allow it to cool down for a couple of minutes, weigh it again, put it back in the microwave.
Repeat. After a couple of circuits, I cut the time back to 60 seconds of microwaving.
When I see the weight change from each session getting smaller than 20 grams or so, I shorten the cooking time again.
At some point, you'll want to start using gloves because the thing gets pretty hot ... shorten the cooking time again.
Once there is no weight change, I stop.
Just realize that at this point the wood is most likely drier than equilibrium, so it's probably a good idea to wait a couple of days before finish turning the piece, because it will re-absorb moisture from the air.