Sorry that still doesn't help. If I create a bitly link here then if you type it in you will get to the website I intend you to. Even though I've (as far as I can tell) not officially registered them being one and the same. I could understand it if bitly maintained a register of these and propagated them through the web so the bitly links were resolved into the new website but that doesn't seem to be what's happening as it takes no time to work and also no time to generate the link - it seems to happen on the client without refreshing the bitly Web page!
Well my understanding is that urls are just ip addresses - direct addresses of computers on tbe Internet, eg 111.222.333.3. To have a nicer URL such as www.stealthpolarbear.com you need to register the URL and it in order for it to resolve to the ip it needs to 'trickle through' the Internet. You can set up sub folders on that URL easily enough but entire new urls always need to do the 'trickle'.
So they must maintain a list of bitly URL | actual URL. I thibk that's what confused me. When I used it the bitly URL seemed to come up without any page refresh as though it hadn't gone to the server at all. Must have done I suppose.