COB question
 

What does it mean if someone says they are going to put your name in because they are doing open biding?

Was this someone from Panhellenic or a chapter that asked for your name for open bidding?

If a chapter did not make quota and/or is under total after formal recruitment, they are eligible to give bids ("open bids") to fill quota and/or reach total. Not every chapter will be participating.

By adding you to a list, either a chapter or Panhellenic may let you know about COB opportunities if any exist.

It was someone from a chapter that said they would put my name in because they still had some open spots. Do you go meet them, or how do they decide to give you a bid in this case?

COR is usually relaxed... the chapters eligable for COR will hold low-key events to give you & the chapter a few chances to get acquainted with one another.

No one here can tell you how they decide whether or not to extend a bid. That is membership selection (MS) and considered private information.