Hello! I was wondering if putting 2-3 inches of straw down then adding some wood chips on it would be a good mulch for a newly planted Bare root apple

There was a study done a few years ago by a horticultural specialist from UNLV. He found that mulching newly planted bare-root fruit trees with 4 to 6 inches of wood mulch made them grow twice as fast as their un-mulched counterparts.

I don't see why the results wouldn't be similar in Minnesota. Keep the mulch at least 12 inches from the trunk of the tree so you don't cause root rot.

I always mulch right up to the trunk without putting the mulch on the trunk. Never had a problem and I've mulched hundreds of trees and shrubs.
And, yes. The wood mulch on top of straw should be fine. I wouldn't pile it too high though because rainfall might run off instead of soaking in. Check under the mulch from time to time to see if soil is staying moist.

I'd stake it down as well.