Great question, Ashleigh!
The Roman Catholic Church is very clear in its teaching against contraception. But the reason they claim this is not because there is particular passages of the Bible that clearly opposes contraception, but because of a commitment they have to a system of ethics called ‘Natural Law’.
‘Ethics’ is just a fancy way of talking about how you decide something is right or wrong. A Natural Law approach to ethics claims that we can find out what is right and wrong BOTH from revelation (i.e. the Bible) AND by using our minds to look at the world and see how it works. Both should give you the same answer. And both must give you answers that are always valid in every circumstance.
The Roman Catholic Church’s position on contraception isn’t based directly on passages that forbid contraception. It’s an argument based on what they claim the purposes of sex are. They claim that sex has both a ‘unitive’ function (that is, sex unites people together) and a ‘procreative’ function (that is, sex is the way that you make new children). Seeing these two purposes for sex (which are both claims that agree with the Bible) they state that each sexual act must involve both of these purposes. A Natural Law approach to ethics seeks to find things that are always true in every circumstance. So if sex is for uniting people, it should always unite people. If sex is for conceiving children, then it should always be for conceiving children. For the Roman Catholic Church, contraception artificially stops the ‘procreative’ purpose of sex, and so is always wrong.
The question we need to ask is: does the Bible speak about sex in this way?
The Bible portrays sex not just as individual acts, but as a vital part of the relationship between a husband and wife. The problem with the approach of the Roman Catholic Church is that it only considers sex as individual acts in isolation. We need to see sex as occurring within the context of a marriage relationship. The Bible often speaks about sex focusing on the ‘unitive’ side of it and not the ‘procreative’ side of it (e.g. 1 Corinthians 7), so it seems the Roman Catholic position makes very strong claims that the Bible doesn’t really seem to make.
So is contraception allowed by the Bible? The Bible assumes that the proper place to have sex is within the loving security and commitment of a marriage (e.g. Genesis 1:25). Within this relationship, it seems quite reasonable that a couple may choose to limit the ‘procreative’ side of their sexual relationship for a limited period of time so that conception is not part of the purpose of every single sexual encounter. Having said that, children are always seen as a blessing from God - so it would seem out of place for a Christian couple to choose never to be willing to be open to having children at all.
Also, it is important to make a distinction between contraceptive methods that prevent conception from occurring and methods that actually abort a foetus after conception has taken place. The Bible sees life within the womb as valuable and created in the image of God, and so abortive methods are not acceptable. If you would like more information about various forms of contraception, please talk to your GP and ask exactly how they do what they do.
I hope that helps - please feel free to ask any more questions you might have.