I'm actually more with Shira on the subject. As a Hebrew native speaker, I am not much familiar with Shakespeare (let alone Shakespeare's English), but I've heard his books had to be translated into modern English so people nowadays will understand them. If you're a native Hebrew speaker, you don't have to read a translation of the bible into modern Hebrew (which I don't think exists), in order to understand it. That being said, it is true that there are some words that are no longer in use, and even some words (not more than one or two though) which we cannot be sure what their exact meaning. Other than that, and some little more additional grammar, it hasn't changed much, as it wasn't spoken much until it's revival.
Of course, some parts of the bible is Aramaic, but it is a different language altogether.
I will say that if you are interested in learning the bible, you should focus on it rather than on modern Hebrew, as it is still different in many ways (not to the extant you won't understand a word).