Moving A Blog As A Subdomain To A Different Server

I was looking at Bluehost as a possible hosting company for my blog which is now a subdomain of my Yahoo Store. They tell me that in order to move the blog, I’ll have to set up a new URL and create a redirect, then move the blog from my existing server to Bluehost and have both URL’s on their server.

Does this process seem like the path to take or is there another way this can be done, keeping the existing URL without creating a redirect?

I’m moving the blog from Yahoo because there have been on going server problems and this is preventing Google bots from crawling my pages.

Thank you in advance.