I need to know what airlines fly NONSTOP from Bloomington, IL to St.
Louis, MO on a regular basis, and vice versa.  I need to be able to
fly from Bloomington, IL to St. Louis on the weekends (Fri to Sun) on
a regular basis with 4 kids - need reasonable airfare.

Nobody doing it at the present time. The cheapest flights are 2 week
advance purchase $186, 1 stop, 3 hrs 27 min outbound and 3 hrs 49 min
return on United Express.  But it's only 146 sm so the best way will
be a charter from STL.  It will take you about 50 minutes non-stop in
a Cessna T210 and will cost about $482 one way + tx for the 4 of you
and your baggage. You determine the time you want to come and go.