Already, there is much buzz about which of Mr. Bloomberg’s anxious competitors will hit him the hardest, and how he will respond. If this week’s skirmish with the Sanders campaign is any indication, the evening could get bumpy. Mr. Bloomberg has a reputation for not taking criticism or unwelcome queries particularly well, once calling a reporter whose question he disliked “a disgrace.” During his mayoral runs, he participated in at least eight debates. He tended to come prepared, data at hand, although he could be prickly and awkward at times. His last turn on a debate stage was in 2009.

Beyond the candidate clashes, this will be debate moderators’ first opportunity to kick the tires on Mr. Bloomberg’s candidacy. They owe it to the public to do a thorough and vigorous job.

Presumably, he will come ready to answer the most overarching criticism: that he is trying to buy the presidency. And he can expect a grilling over his controversial use of stop-and-frisk policing — largely with young black and Hispanic men — while mayor. His apologizing for the practice as he began his campaign struck many as a tad cynical. At the very least, he’ll most likely face some follow-up queries, such as: What took you so long?

There is so much more to explore, both promising — like his new plan to address the cost and quality of college — and troubling — for instance, the widespread surveillance of Muslims by local law enforcement during his time as mayor.

In case the moderators are stuck for material, here are a few lines of inquiry to consider:

Mr. Bloomberg used to be a Republican and, over the years, supported numerous Republican candidates at the state and federal levels. Why should Democrats trust him to champion their values as president?

He once linked the financial collapse to measures taken to deal with the damages of redlining, the practice of banks denying home loans in minority neighborhoods. Does he still believe that?

He has been a longtime champion of gun control. How would he pursue reform if Republicans retain control of the Senate?