Q:

Does an SSL Certificate actually require a dedicated IP?

My web host which I have been with for at least going on 8 years now is requiring a dedicated IP address, which is $3.33/Month now for assigning a SSL Certificate with my web hosting package and website. Now, in the past, they never did this, till they changed their web hosting plans and options. 
In the past, I was able to assign an SSL Certificate by just entering the information required to do so, now I have to pay for a dedicated IP for the SSL Certificate. Even then, that isn't too bad, but it has to be an SSL Certificate through them.
Does an SSL Certificate actually require a dedicated IP address for it to work?
The hosting is Linux and done by BlueHost. I can not get a straight answer from the Customer Support, so I have to ask it outside of that. 
Are they just trying to make more money or are is the dedicated IP a requirement?
Here is the information which I can provide about my web hosting package:

cPanel for the Control Panel
Linux Shared Hosting

A:

SSL certificates no longer require a dedicated IP address.
There is a relatively new technology called Server Name Indication (SNI) that allows SSL certificates to be associated with a virtual host rather than with the server's IP address.   Here is a digicert article that explains it very well.
Your host may not have SNI support installed yet.  It requires newer versions of both Apache and OpenSSL.    Web hosting software such as cPanel may also have to be upgraded before they can allow customers to utilize these features.
SNI also requires client side support.  The most recent version of each major browser now supports SNI.  However, fairly recent old versions may not.   Here is another digicert article about browser support for SNI.  Because some browsers don't support SNI, hosting companies may be reluctant to offer it and instead require that you purchase an IP address with better browser support.
UPDATE: As of 2018, the vast majority of web hosts now support SNI.  The question specifically asked about Bluehost and they now support SNI.  Browser support is even better now because so many sites are secured with SNI.  If a browser doesn't support SNI, you won't be able to use a very large number of HTTPS websites with it. 

