We might see a repeat of something that's happened before--a third party candidate siphoning off votes from one candidate and thus ensuring the victory of the other. There could be challenges to Trump from other candidates---it happened in 2016 on a small scale, in Utah, where the Republicans floated a Mormon candidate as an alternative for those who couldn't stomach voting for Trump but were dyed-in-the-wool Republicans nonetheless (Utah is a red, red, red state).
A less likely scenario is Bernie starting a movement that draws attention--and maybe votes--away from the mainstream Democratic candidate. I think that won't happen for two reasons--one, Bernie's health and age are issues, and two, in 2016, he sucked much of the energy away from the Clinton campaign, and many Bernie-heads stayed home rather than voting for Hillary. That may have helped Trump win, and no one, Bernie included, wants that to happen again.
Trump has made sure that he can't be challenged in the primaries, by the simple expedient of stopping primaries from being held at all in many states. (You know how the Republicans loathe democracy.) However, any challenger might start a third party or run as the candidate for an existing party, such as Libertarian. That candidate would have no chance to actually win, but if such a candidate had been in the running nationwide in 2016 and siphoned off, say, 1/4 of 1% of the Republican vote, Trump would not have won.
The premise I'm making is that any third party candidate would most likely steal votes from Trump, not from the Democratic nominee. People vote for third party candidates as a form of protest--and a LOT of Republicans are feeling shame at the choice they made in 2016 and/or anger that Trump didn't give them the lollipops that he promised. They may be torn between voting for the Orange Orangutan again (cringe-inducing), voting for the Democratic candidate (violating orthodoxy), or staying home altogether (maybe the best choice for them). If Joe Shlabotnik appeared on the ballot representing the Green Grass Party or something, that might be yet another choice for disaffected Republicans.
I don't see many Democrats defecting in such a scenario, though. The party's bottom line has been "Defeat Trump" and it may not matter who the actual candidate is. Though there is the enticing possibility that given recent developments, what they'll actually be trying to do is "Defeat Pence," which would be an absolute walk in the park.