|No, this is not all of the bowls.|
In FBS (Football Bowl Subdivision), there are 125 teams, 82 of which will be in bowl games. FCS (Football Championship Subdivision), which plays for a championship, beginning with 24 playoff teams (FBS has 4 in its title division)
Cutting the field would be extremely easy to do. Start by tossing the losing teams (North Texas, Hawaii, and Mississippi State). Then go to the teams that have feasted on FCS schools, which are the lower level. That includes Army, and South Alabama. Army is 6-5, SA 6-6. One FCS per year is supposed to count toward eligibility (and damn well shouldn't).
There are 17 bowl teams with 6-6 records. Dump them. That, combined with the losers, would immediately drop the number of games to 31 and gives us the minimal competency level of having a winning season.
The big schools, who play 12 regular-season games, also pad schedules with "mid-major" teams, who are not in their leagues, literally, and most often are easy wins for the bigger teams and easy money for the mid-majors.
Eliminate every team that didn't have at least seven wins against FBS teams (those are the Division I highest level programs) and must have won at least four of their last six games. That'd whack half or more of the games instantly. Bigger programs play FCS teams (schools with smaller football programs, though the schools themselves are not necessarily small) to pad their schedules--and their win totals. Those wins should not count toward bowl eligibility.
There are a lot of teams with winning records--my own Tennessee Volunteers, for example at 8-4--who don't belong in bowls. The Vols were 3-4 in their last seven games and lost to South Carolina and Vanderbilt (both 6-6), both terrible. The Vols' defense can't even be called that. They don't belong, but they were a win over Vanderbilt away from being in the high-level Sugar Bowl because the SEC, which provides its second best team there, is laughable.