A better question would be: What does the Bible say about how to get to heaven? Let's establish an answer to that first.
The Bible's teaching is quite clear. The only means of getting to heaven (having eternal life) is to believe that Jesus Christ died on the cross bearing the penalty of your sin and to accept His sacrifice on your behalf. This is all predicated on these simple truths:
1. Man is born into sin and spiritually cut off from God. (Ephesians 2:1)
3. It is not possible to earn a place in heaven by living a good life or by observing any sacraments or pursuing religious goals. (Romans 3:20) Forgiveness of sins is referred to in the Bible a "free gift" meaning it is given apart from anything a person can do to earn it. (Ephesians 2:8-9)
5. Eternal life is granted to all who receive the sacrifice of Jesus on their behalf and place their faith in His ability to save them from their sin. (John 1:12) To those who truly believe, God sends His Holy Spirit by which we are born again. (1 Peter 1:3; John 1:13)
This is what the Bible calls the Gospel, or good news. And it is most certainly that, because it reveals to us that forgiveness of sins comes as a result of God's promise—not as the result of being good or observing religious rites or services.
So, do the teachings of Mormonism and Roman Catholicism create barriers for people to understand this good news? Yes, I believe they do.
Mormonism teaches another Gospel altogether, and Roman Catholicism has heaped hundreds and hundreds of years of tradition and dogma on top of the Gospel so that it no longer resembles what the Apostle Paul preached. But to confidently say that a Mormon or a Catholic will not enter heaven depends on how deeply they have been indoctrinated by those groups. (There are many who call themselves LDS or even Catholic who quite honestly have little or no idea what those belief systems teach.) So is it possible for someone who considers themselves LDS or Roman Catholic to find themselves in heaven? Absolutely!
God doesn't save people according to what church they attend. His only standard is whether or not you are trusting His Son completely for your forgiveness. That and that alone is all that matters.