FWIW, with conference tourneys starting, here are the teams from typically one bid leagues that would grab an at-large bid if they don't win their conference tournament:
Ohio Valley Conference: Murray State 28-2 (#26 in KP). They are a lock to get in.
Missouri Valley Conference: Loyola-Chicago 22-7 (#29 in KP). Not a lock, but would probably get a bid if they don't win the MVC.
Atlantic 10: Davidson 24-4 (#45 in KP). Not a lock, but they do have a neutral court win over Bama.
Atlantic 10: Dayton 20-9 (#49 in KP). Horrendous to start the year; among the youngest team's in the country; no program was more screwed when the 2020 tourney was cancelled (likely #1 seed); has neutral court wins over Kansas, Miami, and also beat VT.
Also, the West Coast Conference (Gonzaga's conference) is going to grab its most bids in conference history. Zags, St. Mary and SF are in. BYU is on the bubble.
Similarly, the Mountain West typically will grab more bids than usual. San Diego State, Colorado State and Boise are in. Wyoming is likely in. Not impossible for Fresno or UNLV (they host) to win the conference tournament.