data in onActivityResult is null

in A onActivityResult method

   if(null!=data){

    Bundle bundle = data.getExtras();
    String mydate = bundle.getString("Date");

   }

and in B

Intent returnIntent = new Intent();
returnIntent.putExtra("Date",dateSelected);
setResult(RESULT_OK,returnIntent);      
finish();

try this:

Then, in B, I do:

Intent intent = getIntent();
intent.putExtra("Date",dateSelected);
setResult(RESULT_OK, intent);
finish();

And, in A:

@Override
protected void onActivityResult(int requestCode, int resultCode, Intent data) {
    if(resultCode == RESULT_OK && requestCode==1) {
        Bundle MBuddle = data.getExtras();
        String MMessage = MBuddle.getString("Date");
    }
}

I know this is answered, but just to give more explanation on the error, you were using getIntent() instead of the data element received on the callback.

getIntent() returns the Intent that was originally used to open Activity A (maybe when you opened the app or from another activity), and data is the intent that Activity B returned as response parameters.

Also, you were using getIntent() in Activity B instead of creating a new Intent that would be returned to Activity A.

Intent returnIntent = new Intent();

Finally, the created intent must be added in setResult

setResult(RESULT_OK,returnIntent);