What is the shape seems lots of girls' hats have these days. Is it called the bull rider? The crown in almost rounded and the hat sits really low on the head 

Got any pictures you can post for referance? 

I have a wider square crown on my straw and my felt.  I have always had trouble getting a hat to fit and look good.  I have a bigger head and forehead specifically and everything looked “perched” and goofy.  Found the straw shaped like that and loved it - flattering on me.  Had my felt done the same way.

a more open crown like that does allow you to pull the hat down tighter and less likely to come off.  A lot of girls would “pop” the crown in their hats to pull it down - having it shaped with a more open crown saves you that trouble.