Domain names are purchased on a yearly basis. Once you pay for it, you own it for that year. Because it is a lot of work and time to make the switch, domain registrars place a limit on how often you can move the management company. But you do not have to have your domain name and your hosting with the same company. Mine have been with separate companies for several years now.
Until your domain name has aged enough so you can transfer it, all you need to do is change the Primary and Secondary Name servers to point to your new hosting. Once that's set up, there isn't much more to do. Manage your domain name from Bravenet and your hosting from where ever that is.
There is nothing strange about your new hosting working. Clear out your temporary internet files or force a couple of browser refreshes and your site will respond with, or without, the "www".
