This may seem odd, but make sure they study the bible. Many bible groups actually study man written book about the bible. When I joined my group this was the case. I gently encouraged the group to change to the bible and we did John's gospel and now Acts.
But the leader again is privately talking to group members and trying to take us away from the bible. I am aware she is looking for an opportunity to talk to me.
I am aware in other churches locally, bible study is actually not bible study but the study of man's thoughts/ writings, with occassional bible references.
Another good example is the non- Christian organisation, the Jehovah's Witnesses. Their study is all done through books and magazines produced by the organisation, instead of directly through the bible - which in their translation has serious differences to every well known translation.
I hope and pray this bible group has nothing to do with any organisation/ groups that are not mainstream 'trinity' believing Christians.
A Christian background can be good or bad. Ours is a personal faith. A personal relationship with Jesus Christ. The church is the worldwide body/ family of Christ. But this is not a get out clause for not being in a physical church of believers -actually the reverse! I spent 10 years in rebelion to our Lord, hiding behind my daily bible reading and critising church goers.
So my advise on the bible group, is find out if they are studying God's Word/ the bible. If not ask Why? Is God's Wisdom not good enough, that they need man's cleverness to suppliment it!
But I advise you to look into joining a mainstream church and doing the bible group through that church. Putting yourself under the authority, love and protection of the authority of that church. Having mature Christian friends, makes social times so much easier to be safe from attacks of our enemy. You can learn how to pray, how to worship/ praise - it's like a fast track of Christian learning. 
Lastly may I ask how You know you are a Christian? Please don't be insulted by the question. God bless, SofTy.
1 Corinthians 1:12-13 Now this I say, that every one of you saith, I am of Paul; and I of Apollos: and I of Cephas; and I of Christ.
Is Christ divided? was Paul crucified for you? or were ye baptised in the name of Paul?
KJV
May the power of the Spirit of our God unite us. SofTy.
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