BitNami Java stacks cannot be installed on top of BitNami Tomcat stack. So, it is perfect for your purpose to use the BitNami Liferay stack.
First step will be install the stack on your hosting provider. Then, create a backup of the database at your localhost to move it to your production server as described below:
You can also use the same path and user on your host provider. That way, you can copy the entire folder (keeping in mind the permissions an symbolic links) to your production server. To do so, you can follow the same approach described below for a full backup, but restoring it in your production server.