It's an oversimplification to see Bradley as "more liberal" than Gore in 2000, at least in his support: " Ironically, Bradley's message doesn't seem to be resonating yet nearly as much as his loping, antipolitics (and implied anti-Clinton) persona; in many surveys, Bradley is running better among independents and moderate-to-conservative Democrats (many of them disillusioned with Clinton) than he is with liberals. " http://prospect.org/article/more-liberal-you-thought Also note that Gore attacked Bradley's health plan as "abolishing Medicaid."
IMO Monicagate and the impeachment attempts greatly helped Clinton (and by extension Gore) among liberals and minorities. Clinton came to be a liberal hero--which he had not really been previously (and would not be in the future). And in particular, blacks stood by Clinton in the impeachment crisis and appreciated Gore's association with Clnton. Evan Bayh did not have the same sort of longtime Clinton connection.
Bradley may have been a bit to the left of Gore as a US senator--though both were basically centrists--but that was mainly a matter of the different states they represented. And by 2000, Gore had come a long way from being the conservative Democrats' choice he was in 1988. In particular, he had gotten a reputation as an environmentalist (though Bradley attempted to challenge it). Meanwhile, while the DLC did support Gore, it worried he was going too far in remaking himself and becoming too "populist"--Al From expressed fears on that score as early as 1999. http://articles.sun-sentinel.com/1999-10-13/news/9910120572_1_gore-s-support-dlc-bill-bradley
Liberals didn't see Clinton as a "liberal hero" they just didn't like the conservatives Republican congress trying to kick out the president they voted for and supported on MOST (not all) issues. So many liberals did defend Clinton indeed, but I would not say he was seen as some sort of liberal hero at any point during his presidency. If anything by 1998-99 Democrats and liberals were tried of having to defend Clinton over his many scandals. Some were clear witch hunts, but some of his scandals were self-inflicted and liberals felt they ultimately hurt the Democratic Party and took more attention and time away from the issues liberals cared about. Issues that Clinton and the Democratic party were not addressing at the time. Mostly because so much time and political resources went towards defending Clinton and putting out Clinton's fires.
Because of the DLC's dominance over the party in the 1990s and 2000s is precisely the reason I see somebody like Evan Bayh getting the Democratic nomination in this TL.