mrmom,
I would encourage you to ask this question on the message boards at d3baseball.com.
They have some folks who really know this stuff.
The short answer is that in d3, at large is called Pool C and Pool B.
There are 3 Pool B bids which come from the schools who are independents or in a conference with not enough teams to be recognized for Pool A.
The Pool C is every other school which did not get an automatic berth, usually by winning the conference tourney.
In d3, travel cost and distance is everything, at least as important, if not more so than W/L's, strength of schedule/RPI. It is not the "best" 15 Pool C teams which get berths/invited. Money and travel play a role also.
With that said, there is some movement of schools out of region. Not a great deal, but some...perhaps 1 to as many as 3 schools in a year, but sometimes none.
In general, the Pool C's are not announced until the early morning hours on a Monday in mid-May, and, if selected, they will be playing at some location by Wednesday.