Asked about the criticism of Mr. Bloomberg’s vast wealth — and his decision to self-fund his campaign — Ms. Sheindlin cast it as a political strength, saying he “holds no constituency other than the people who elected him.”

Her first journey through the rigors of a day on the presidential campaign came on Saturday, when she joined Mr. Bloomberg on a bus tour across Texas. It was Ms. Sheindlin’s first face-to-face meeting with Mr. Bloomberg, whom she had previously only spoken with over the phone.

“I know Mike through his work,” she said. “Today is really the first touching of the flesh for us.”

Swapping her signature lace collar for a stylish scarf, she walked through a line of selfie-snapping voters to board Mr. Bloomberg’s campaign bus, emblazoned with the slogan “Get It Done Express.” She ordered brisket at a barbecue joint. (“No bread,” she sternly instructed.) And she smiled through Mr. Bloomberg’s awkward campaign trail prattle.

“I’m never sure whether it’s appropriate to kiss the judge,” said Mr. Bloomberg, taking the stage in San Antonio after Ms. Sheindlin’s introduction. “There’s nobody this country respects any more than you — there are other people as well — but you really are a great American and you should be very proud of what you do.”

While Ms. Sheindlin did not mention any of the candidates by name, her judgments on the Democratic primary field were rendered quite clearly for voters. She implied that former Vice President Joseph R. Biden Jr. was a “nice guy” but described him as “number two,” when the country “deserves a number one.” Her comments denouncing calls for “revolution” were a shot at Senator Bernie Sanders of Vermont.

Aides to the former mayor said that Ms. Sheindlin’s support arrived through a totally organic process. “Judge Judy Sheindlin is known for her good judgment,” said Galia Slayen, a spokeswoman for Mr. Bloomberg.