I think a lot of good advice, both as to structuring a Bible study and being sensitive to other members of one's chapter, has been given here. But I would add a few more things.
First, everyone involved should have a clear distinction between personal spiritual growth and evangelism/"speading the gospel." A chapter Bible study should be about the former, not the later. That should be made clear to everyone in the chapter.
Second, there is a distinction between inviting people and letting people know they are welcome. Everyone should know they are welcome. No one person should be "invited" unless the "invitor" is already fairly sure they would be interested.
Third, just as some have noted that this all might be more common and acceptable in the South (or perhaps at church-related colleges as opposed to public colleges), I think differences between Greek groups needs to be taken into account. (Refer to Erik Conard's post
Fraternity Histories, read 'em.) The "culture" of your particular GLO (not to mention your chapter) might have a bearing on how a Bible study should be approached and would be received.
Many threads on GreekChat have noted how some groups -- Phi Sigma Sigma and Delta Phi Epsilon come to mind -- were founded with non-sectarian principles, and that might affect how a Bible study would fit into the chapter. And of course, there are the traditionally Jewish GLOs.
Perhaps at the other end of the spectrum there are groups like Alpha Tau Omega. It, like many other fraternities of its founding era, was founded upon "Christian Principles," but unlike many GLOs, ATO still stresses a distinctively spiritual, faith dimension. As ATOtnBetaTau pointed out, ATO publishes an "ATO Devotional Book." It also has a national Spiritual Leadership Consultant, an Outward Bound-type spiritual leadership program (
Noah's Ark) and an
ATO Prayer Web on its national website. Quite a different environment for suggesting a Bible study.