I'm afraid I have no idea why you're unable to install plugins.
If you correctly installed the WordPress software at Bluehost and you have access to the WP-Admin dashboard you should be able to install plugins. If you're not able to, either your host is blocking it, or there's something wrong in the PHP files for your site.
For help with that you'll need to ask in the self-hosted forums if Bluehost support is not able to help you. We can't help with self-hosted sites in this forum as those sites are not on our servers and we don't have any access to them.
You can find the self-hosted forums here: https://wordpress.org/support/