If the only divergence is Bubba declares, then on the back of Hart's destruction, Clinton's personal baggage would destroy him in short order in the tabloid-fever atmos of 1987, which is the year when politicians personal lives became fair game, but which still could retain the disapproval of extra-marital stuff from the earlier era. But even in the OP's scenario, if we're talking about potential divergences, Clinton is a prime candidate to replace Hart's position in the historical record.
Even in 1992, Clinton's candidacy went into an absolute tailspin with Gennifer Flowers; and that was after years of a backlash toward the media for what happened to Hart, which afforded Clinton an insulation Hart lacked - even then, Clinton's untrustworthiness dogged the campaign. The continued popularity of this subject on here shows that people really don't understand the dynamics of what was going in 1987; there's no way Clinton would have made it to the actual voting of the following year had he declared, still less win the nomination and be elected president.