**Core Concept**
Bipolar staining is a characteristic feature of certain bacteria that exhibit a "safety pin" or "kidney bean" appearance under the microscope. This phenomenon occurs due to the presence of a thick capsule and the partial decolorization of the cell wall, resulting in a distinctive appearance.

**Why the Correct Answer is Right**
_Bordetella pertussis_, the causative agent of pertussis or whooping cough, exhibits bipolar staining due to the presence of a thick capsule and the partial decolorization of the cell wall. This unique staining pattern is a key diagnostic feature of _B. pertussis_. The organism's ability to adhere to the respiratory epithelium and produce toxins, including the pertussis toxin, contributes to its pathogenicity.

**Why Each Wrong Option is Incorrect**
**Option A:** *Yersinia pestis*, the causative agent of plague, typically exhibits bipolar staining, but it is not associated with coughing bouts in a 4-year-old child.
**Option C:** *Streptococcus agalactiae*, a group B streptococcus, does not exhibit bipolar staining and is not typically associated with pertussis-like symptoms.
**Option D:** *Klebsiella pneumoniae*, a gram-negative rod, does not exhibit bipolar staining and is not typically associated with pertussis-like symptoms.

**Clinical Pearl / High-Yield Fact**
Pertussis is a highly contagious respiratory illness that can spread even among immunized individuals, highlighting the importance of maintaining herd immunity through vaccination.

✓ Correct Answer: B. B. pertussis