I have sites at BlueHost and I will try to help you sort things out.
After downloading wordpress 4.2.2 via my bluehost account
Does that mean you used a cPanel script to do your WordPress installation?
the confirmation email from the (script installation?) entails my new admin url, which directs me to my old wordpress.com admin page.
Do you have a registered domain name and URL that is still pointed to the wordpress.com servers? If so, you will need to go to your wordpress.com Dashboard and point your domain to the BlueHost nameservers, then go to the BlueHost cPanel and assign your domain to public_html. And then if you have installed WordPress in a sub-folder, you will need to either move it to public_html or do some different file moving and editing or use this .htaccess (my own preference) in public_html:
## from https://my.bluehost.com/cgi/help/347#redirect
# .htaccess main domain to subdirectory redirect
# Do not change this line.
RewriteEngine on
# Change example.com to be your main domain.
RewriteCond %{HTTP_HOST} ^(www.)?example.com$
# Change 'subdirectory' to be the directory you will use for your main domain.
RewriteCond %{REQUEST_URI} !^/subdirectory/
# Don't change the following two lines.
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
# Change 'subdirectory' to be the directory you will use for your main domain.
RewriteRule ^(.*)$ /subdirectory/$1
# Change example.com to be your main domain again.
# Change 'subdirectory' to be the directory you will use for your main domain
# followed by / then the main file for your site, index.php, index.html, etc.
RewriteCond %{HTTP_HOST} ^(www.)?example.com$
#RewriteRule ^(/)?$ subdirectory/index.html [L]
## index.php for WordPress
RewriteRule ^(/)?$ subdirectory/index.php [L]
https://my.bluehost.com/cgi/help/347#redirect
