not getting a bid

Very, very uncommon.

If you go through formal recruitment and maximize your options, it is very likely you'll get a bid. Maximizing your options means keeping an open mind to EVERY house and being willling to accept a bid from any house that gives you one.

The vast majority of girls who don't end up in sororities are ones who drop out of rush. Any girl that says they "didn't get a bid" really just means she didn't get a bid from a house she wanted. The process is designed so that as long as you meet the minimum requirements for formal recruitment, you are "guaranteed" a bid. And even girls who don't meet the minimum requirements, (girls with under a 3.0 gpa) still get bids.

This doesn't mean that there are no girls who get cut completely. It still happens. But it's rare.