According to SB Nation, the CUSA bowl tie ins are:
New Orleans - Sun Belt
New Mexico - Mountain West
Boca Raton - THE AMERICAN!!!!!!!!!!
St. Pete - THE AMERICAN!!!!!!!!!!!
Bahamas - MAC
Heart O' Dallas - Big 12
Any further teams would be taken care of by the fact that most of the P5 have more slots than they generally can fill, CUSA would get the Liberty Bowl if either main league (SEC/Big12) cannot fill it, followed by other slots.
We had this discussion a few years ago. Correctly, IMHO, we took one of the Florida bowls over playing a 6-6 P5 team in Dallas before nobody. Several got their panties in a wad over it, but the same thing will happen if the situation arises, this year or any other year as long as this is the system.
In any event, it seems like the league has us penciled in to take one for the league and go to the Bahamas. It is what it is.