Just a minor correction to start: the "Mormon Bible", at least for English speakers, is the King James Version of the Holy Bible, just like many other Christian denominations. :) 
 
The Book of Mormon is an example of an additional book of scripture. It is not necessarily a "later revelation" though. Rather, it is a book of scripture given to a different set of people. The Old and New Testaments were given to people living in parts of Europe and the Middle East. The Book of Mormon contains scriptures given to people living in the Western hemisphere, but during some of the same time periods. For example, the bulk of the Book of Mormon covers the time period from roughly 600BC to 400AD, although there are other parts that cover a much earlier time period. 
 
One purpose of the Book of Mormon is to confirm the truth of the Bible. We live in a day where fewer and fewer people are believing in the Bible. And of those that do believe in the Bible, there is a great deal of disagreement around what its teachings are. Some people who claim to believe the Bible, for example, believe that Jesus was only a great teacher and not necessarily the Son of God. The Book of Mormon then, as another witness of Jesus Christ, helps confirm the truths of the Bible and clarify doctrines that people have come to twist due to ambiguities in the Bible. 
 
For a few examples, in the Book of Mormon it is made very clear that the mode of baptism is by immersion, not sprinkling or any other method. It reinforces the idea that little children are pure and have no need of infant baptisms. It testifies quite clearly that Jesus Christ is the literal Son of God and the only means of salvation. These doctrines are also found in the Bible, but you are probably aware that there is also a fair amount of debate around them too. 
 
If you take a step back and ask yourself, "what is the Bible, really?" the answer is that it is a record of God's dealings with mankind. There's a pattern - God speaks to someone, and the words He speaks are recorded as revelations and, if recorded accurately, they are considered scripture. Likewise, God calls prophets to teach the people. The words of these prophets get written down and, if recorded properly, these too are considered scripture. So it's not at all "bad" that there is more than one book of scripture - if nothing else, it's just proof that God loves all his children and wants all of them to learn about Him and His plan for them. 
 
We do not believe that God has stopped caring about his children. For that reason we believe that neither the Bible nor the Book of Mormon represent all scripture that God ever has or ever will give. In fact, even today there is a living prophet on the earth, so the same pattern continues: revelations and teachings of prophets are written down so we can study and cherish them. These writings are scripture. 
 
Anciently God cared for His children so He sent prophets to teach them. God doesn't change, so it follows that not only does He still care for His children, but also that He still sends prophets to teach them. It would be really hard for me to believe that He has stopped that pattern or changed in some way. Both ideas seem to contradict what the Bible teaches. 
 
To answer your questions specifically: if a person has satisfied the requirements for salvation, as provided in the Bible, then yes, we consider him to be saved if he endures to the end (you can't just e.g. get baptized and become wicked and still consider yourself done, since obviously the Bible teaches against that). We do believe, however, that one of those requirements is that a person must be baptized by one having authority from God. So among other things you need to find someone who actually has authority from God, otherwise the baptism obviously wouldn't be recognized by God as being valid. The Book of Mormon helps you find such an authorized servant of the Lord. 
 
Also, while we love the Bible and use it constantly, we don't believe that the Bible as we have it today is necessarily as complete as it was when it was originally written. It has been translated dozens, if not hundreds, of times, and has passed through many hands. Prominent non-Mormon scholars have documented literally *thousands* of changes to the Bible in just the translations we know about. If you are unaware of this, I urge you to spend some time reading the known history of the Bible. It's fascinating. To me it's a miracle (literally) that we have the Bible in as good a form as we do, but at the same time one has to admit that it has undergone significant.. um.. revisions throughout the ages. :) And all that is just what we know about from recent history - who knows what other additions or removals have happened that we don't know about. 
 
So why did God feel it necessary to provide a later revelation? Well, because He still loves all of us! I think it's obvious that no single book (or even a building full of books) is going to tell us even a fraction of God's knowledge, so Him giving us more isn't so much an indication of deficiency in what we already have as a testimony that He is alive and still cares and wants us to learn more.