I would like to make this question more specific based on what the name should mean. The name is for a group that actually follows the moral ideas of the Bible. This means that the name must be specific to the Bible. Based on this, which of these names do you like?
I will briefly comment on each name.
On the plus side, "Bible Followers" is a simple and easily understood name. On the minus side, it isn't precise. It isn't clear whether one follows the beliefs of the Bible or the morals. This name is also fairly generic and not very memorable.
On the plus side, "Act Biblically" clearly describes what members should do. And it is a fairly memorable name. On the minus side, it isn't a noun so it can't be used as a label for the group or its members. So for example, members here can refer to themselves as CoAlphas, but there would be no similar way for members of "Act Biblically" to refer to themselves.
On the plus side, "Scripturist" is the noun that most accurately describes members of this group. The definition of scripturist is "One who is strongly attached to, or versed in, the Scriptures, or who endeavors to live by them". "Scripturist" is also short and unique. On the minus side, it is obscure and may be difficult to spell.