But Mrs. Clinton has not picked on Mr. Bush at random: Her aides, for the most part, believe he is likely to ultimately win the Republican nomination. And in a very crowded Republican field, in which Donald J. Trump is sopping up the news media’s attention, Mr. Bush has for the most part escaped the kind of sharp elbows that would normally have been thrown at such a high-profile candidate.

Mrs. Clinton seems happy to pick up the slack. She faulted his record on voting rights. She ridiculed him for saying that Americans need to “work longer hours.” And she went out of her way, in a CNN interview, to point out that Mr. Bush no longer supported a path to citizenship for undocumented immigrants.

The feistiness lives up to Mrs. Clinton’s promises to be a “fighter,” and could help satisfy liberals who want her to show aggressiveness on behalf of their ideals.

“For months now, she has been a piñata for the Republicans, the Koch brothers, the press and anyone else who wanted to take a swing,” said Paul Begala, a strategist in Bill Clinton’s 1992 campaign. “Hillary is a great counterpuncher, and I am glad to see her fighting back. Democrats will see she is not from the surrenderist wing of the progressive movement.”