**Core Concept**
The question requires identification of a gram-negative bacterium that exhibits bipolar staining with methylene blue, which is characteristic of certain pathogenic bacteria. This is a classic example of a clinical microbiology scenario where the presentation of multiple abscesses in a diabetic patient, combined with the specific staining properties of the bacteria, guides the diagnosis.

**Why the Correct Answer is Right**
The gram-negative bacteria that exhibit bipolar staining with methylene blue are typically _Francisella tularensis_ or _Bartonella_ species. However, in the context of multiple abscesses in a diabetic patient, the most likely causative agent is _Bartonella henselae_, which is known to cause cat-scratch disease and is often associated with abscess formation. This bacterium invades and replicates within endothelial cells, leading to the characteristic bipolar staining pattern.

**Why Each Wrong Option is Incorrect**
* **Option A:** This choice is not relevant to the scenario described, as the bacteria in question are gram-negative, not gram-positive.
* **Option B:** This choice is incorrect because the described staining properties do not match those of _Staphylococcus aureus_.
* **Option D:** This choice is incorrect because the described staining properties do not match those of _Escherichia coli_.

**Clinical Pearl / High-Yield Fact**
Diabetic patients are more susceptible to infections caused by opportunistic pathogens, including _Bartonella henselae_, due to their compromised immune status. This is a critical consideration in the differential diagnosis of skin and soft tissue infections in diabetic patients.

**Correct Answer:** C. _Bartonella henselae_