I figured out how to enable the uploadprogress library in Bluehost's shared hosting environment. Being as there was not much documentation on this anywhere on the web, I decided to put it down in a blog post. 

1. Make sure you have your own PHP.ini file so you can easily make changes. Do this by following the instrcutions here: https://my.bluehost.com/cgi/help/128
2. Log in to your account via SSH
3. Ensure you have the uploadprogress.so library in /usr/lib/php/extensions/no-debug-non-zts-20060613. If you don't, you have to contact technical support and ask them to install it on your account. They will do this, but they don't guarantee that it will work. 
4. Edit the php.ini file you created in step 1 and add extension=uploadprogress.so
5. Save, exti, and check your drupal site's status page. You should be all set.