How is anyone supposed to understand the Bible if it is written in such English that modern English speakers don't speak?

That’s why newer translations have been made. 

The error made by the KJV only crowd is that they forget that some English language words have changed meaning over time and others have either fell into disuse (hence the poorer comprehension of non native speakers).They also forget that English uses some words to have multiple meanings. 

Try a contemporary version, such as the NIV, ESV, or NASB.

I'm a “modern English speaker” and I understand it. The problem comes when people want what it says to be more reasonable or believable or to say something it doesn't. Then the claim is made that people just don't understand it.

Umm, there are many versions of the bible.

The Bibles translated in the 16th and 17th centuries, such as the King James and the Douay-Rhiems are written in early modern English, the language of Shakespeare, Marlowe, Jonson and others, and are more difficult for modern readers not familiar with the language of 400 years ago to understand. Fortunately there are many better translations of the Bible written in modern English that are easy to understand. 

Procure a newer version like NLT, CEV, NIV, BBE etc. 

Actually it was written in Greek. Bibles in all other languages were translated from the Greek. There are several excellent English translations. The one you are referring to, the King James Version, is not only in Old English, but is also the poorest translation still in common use. The translators appointed by King James were simply not expert in the ancient languages, and it shows, on almost every page. You can find several accurate and easy to read translations of the Bible at any Catholic book store. And, it will be the complete Bible, with the original 73 books, unlike the King James, which is missing 7 of the original books.

Here's a thought: read a newer translation than the King James Version. Not that I need to. Some of us have no trouble understanding it.

You should attempt to read it in Greek and Hebrew, not in English, so the question is irrelevant.

King James had it translated from Greek, Latin, and Hebrew, so normal people could understand it.  ou can google the rest.