BYU can only play in bowl games that end up with an opening. I believe every bowl game this year has a contract with at least two conferences and many have contingency contracts in case one of their conferences doesn't have enough teams.

The Cheez-It Bowl for example takes a PAC 12 team and a Big 12 team but has an agreement to take a MWC team if the either conference can't feel their spot (Boise State filled in for the PAC 12 in 2016). BYU's only chance to play here would be if both the PAC 12 and the Big 12 failed to supply a team.

The MWC only has five bowl games (six with the Cheez-It Bowl). They currently have 4 teams with 6+ wins plus Boise State at 5-2 and Nevada has 4 wins and I would expect they will be favored in 3 of their last 4. The MWC will likely fill all their slots. If they do have an extra slot it would likely be the Potato Bowl, New Mexico Bowl, or Arizona Bowl. Best chance for BYU to get an MWC bowl bid would be some combination of an MWC team taking the NY6 spot, the MWC only getting 5 eligible teams, and/or the MWC getting a team in the Cheez-it Bowl.

The PAC 12 has 7 bowl tie-ins (plus the possibility of 8+ if they get an NY6 at-large bid). Oregon State won't make a bowl and I would bet against UCLA, Arizona, ASU, & Cal as all would need 1+ upset(s) to reach six wins. If all five of these teams fail to get six wins, the PAC 12 would only have 7 bowl eligible teams. If they got a 2nd NY6 game, they could have an opening (likely the Cheez-it Bowl) but again the MWC will get first rights to that one if it is available. I don't believe the PAC 12 has a true pecking order so they may elect to leave another bowl game open (Las Vegas Bowl???). If the PAC 12 leaves another game open, BYU could take it.

The Big 12 may have some openings for BYU. They have 7 bowl spots (plus any additional NY6 or playoff teams). Kansas won't make a bowl but everyone else has at least 3 wins so far. If they did have an opening, it would likely be the Armed Forces Bowl.

The ACC appears to have 10 bowl tie-ins (plus two contingencies) for 15 teams (including Notre Dame). 12/14 ACC teams are within 1 game off .500 or better. The conditional tie-ins would be for the Birmingham Bowl or the St Petersburg Bowl.

The AAC has seven bowl tie-ins plus two contingencies (Independence, Liberty) and an NY6 possibility. Five of their 12 teams currently have 5 or more losses so they will likely have some openings. Their Independence Bowl contingency appears to be shared with Conference USA. The AAC may choose to put one of their better teams in the Independence Bowl or Liberty Bowl and leave one of the lower tier bowls open.

I may try to figure out BYU's path to different bowls in the next few weeks. It's really to early guess at this point what may happen over the next six weeks and there are so many moving pieces.