The two biggest conferences in college sports say they do not support the current version of a bipartisan bill designed to regulate an industry struggling for answers in a quickly changing era in which some players make millions.

It’s unclear whether some of college sports’ other biggest stakeholders—namely, the Big Ten, SEC, and NCAA—will endorse it.

The two biggest conferences in college sports say they do not support the current version of a bipartisan bill designed to regulate an industry struggling for answers in a quickly…