question

Bumping so that someone might answer.

For fraternities it can take a few months or a few years. It comes down to meeting national requirements: chapter size, housing, gpa, etc. and each national organization has different requirements. My chapter took 4 years to get our charter and meet national requirements but that was 100 years ago

A team of Tri-Sigs will probably start publicizing the sorority all over campus for a few weeks. Then they will probably conduct a couple of general information meetings for anyone interested. At those, women can sign up for interview sessions with sorority members.
There may be a second interview session with team members (the team is often made up of sorority national and regional officers and sorority consultants, who are just-graduated sorority members trained to work with chapters.
Often another chapter comes in to conduct a preference-type party, and then the sorority delivers bids.
More new members may be added over the next two or three weeks.
The chapter is generally installed 8 weeks or so after bids go out. Consultants and national offices continue to work with the chapter after initiation.