Installing Drush on the shared hosting server, such as Bluehost, is tricky. Here's what I did for Bluehost.
1. Install Composer
curl -sS https://getcomposer.org/installer | php
In my case, this created composer.phar on the home (current) directory. Moved it to ~/bin.
2. Check if composer runs
For some reason, simply running composer.phar causes an error. Instead, run the following.
If successful, it shows the version and usage.
3. Install Drush
php-cli bin/composer.phar global require drush/drush:dev-master
dev-master may be 6.* if you want version 6 of Drush.
4. Add Drush path.
This is another tricky issue. Somehow, drush is installed the following directory.
Note the double /drush subdirectory. The path should be pointing to the directory in .bash_profile.
5. Run drush
If the path is correct, simply running drush will show the usage.