Unfortunately, the most effective way to achieve your goal will be to use the command line.
Since you have a "dedicated IP address," you should be able to gain access to the command line fairly easily using the instructions found here:
Bluehost Web Hosting Help - SSH Access
You will need to enable Sudo Access:
Bluehost Web Hosting Help - VPS or Dedicated Hosting - Enabling Sudo Access
According to Bluehost:
The Bluehost system is setup with CentOS and is currently not compatible with any other OS configuration.
Therefore, you will need to use
yum to install Let's Encrypt on CentOS. Here's a beginner guide to using
yum on Bluehost:
Bluehost Web Hosting Help - VPS or Dedicated Hosting - Using yum
And here is a very helpful guide for how to install Let's Encrypt on CentOS:
How to Secure Apache with Let's Encrypt on CentOS 7
If this task is too difficult, then I would recommend either transferring to a host that allows more flexibility, such as Digital Ocean, or simply purchasing a commercial SSL Certificate:
Bluehost Web Hosting Help - Purchasing or Renewing SSL certificates