how to change hosts but keep domain name with wp?

I’m trying to move my blog from Freehostia to Bluehost but I am totally lost.

My blog address is https://johnbentleyswriting.com

The blog, hosted in Freehostia, uses wp script. First I created a backup file in the Freehostia server & tried to import it via the Bluehost wp installation feature / it said “installation not found”.

Then I decided to try a new installation of wp in Bluehost. It installed the script and assigned me a new password for the same wp login address. I went into the login url & of course it detected the old account, set up in Freehostia. I logged out and typed in the new password and it told me it was incorrect.

Does anyone know how to transfer a blog from one host to another, but without changing the domain name? Bluehost refuse to provide any support – they just point me to a tutorial which tells me how to export / import an .xml file but doesn’t answer the issue about the login.