Robert, I'm not familiar with your turning experience, so please forgive me if this is 'beneath you.'
Are you asking whether to turn it with a natural edge, i.e. bark side is the top, or in the conventional manner for a utility bowl, i.e. bark side is the bottom?
What size is your blank?
Is this wood 'valuable', such that you want to get as many bowls out of it as possible, and are considering coring?
If you mount it with a face plate or screw chuck, however the flat side is cut will determine the features that will be included and the quality of the finished bowl. Did you cut the blank, or recut the flat side, to suit your idea for the best possibly bowl? If someone else cut it, do you think they did a good job?
If you mount it between centers, you can adjust the orientation of the wood as you begin turning which allows you to get the best possible finished piece--not the biggest finished piece, but the best. To do this, your lathe and blank need to be a good match in size, and you have to be comfortable cutting wood-air-wood-air.