What the Bible does say
I think there can be exceptions to living together with your girlfriend since this is not explicitly dealt with in the Bible. *So, in some cases it would depend on how the couple personally felt convicted by their actions. *That said, please please please check yourself, and don't be timid about asking your partner to check the themselves with these as well.
1 Corinthians 7:9
But if they cannot control themselves, they should marry, for it is better to marry than to burn with passion.
1 Corinthians 8:13
Therefore, if what I eat causes my brother or sister to fall into sin, I will never eat meat again, so that I will not case them to fall.
Romans 14:21
It is better not to eat meat or drink wine or to do anything else that will cause your brother or sister to fall.
Matthew 5:28
You have heard it was said, "you shall not commit adultery." But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart.*
Proverbs 6:25
Do not lust in your heart after her beauty or let her captivate you with her eyes.
Two words of caution: *The devil lures us into temptation and when the opportunity is present, he attempts to kick down the door with everything he has. *
Even though a couple may keep themselves pure, while under the same roof, they still may be 'seen' to be encouraging other Christians to live together before marriage. *Considering how easy it can be to step over the line when things 'get heated', living together can be too much of a stumbling block for most. *Couples should consider how they will feel if they do keep themselves pure, but later find out that their actions encouraged another Christian couple to live together, but they end up falling into sin. *Maybe this is a sister, a brother, or even one of their own children years down the road.