First things first: a bruise (layman's term) is a type of hematoma (medical term), by definition.1
Rubbing a bruise is not a part of the standard protocol for treating hematomas. The standard is RICE, which stands for Rest, Ice, Compression, and Elevation.2
Several sources suggest that rubbing and other forms of massage in general may actually contribute to tissue damage.
See "Hepatic Hematoma after Deep Tissue Massage" in The New England Journal of Medicine, "Massive Haematoma from Digital Massage in an Anticoagulated Patient: A Case Report" in Singapore Medical Journal, and "Haematoma Testes due to Traditional Massage in a Neonate," in Tropical Doctor. 3,4,5,6
- From Wikipedia: "A bruise (layman's term), also called a contusion (medical term), is a type of hematoma of tissue in which capillaries and sometimes venules are damaged by trauma, allowing blood to seep, hemorrhage, or extravasate into the surrounding interstitial tissues."
- Ernst, E. “The Safety of Massage Therapy.” Rheumatology (Oxford, England) 42, no. 9 (September 2003): 1101–6.
- Trotter, J. F. “Hepatic Hematoma after Deep Tissue Massage.” The New England Journal of Medicine 341, no. 26 (December 23, 1999): 2019–20.
- Yeo, T. C., M. H. Choo, and M. B. Tay. “Massive Haematoma from Digital Massage in an Anticoagulated Patient: A Case Report.” Singapore Medical Journal 35, no. 3 (June 1994): 319–20.
- Ram, S. P., K. Kyaw, and A. R. Noor. “Haematoma Testes due to Traditional Massage in a Neonate.” Tropical Doctor 24, no. 2 (April 1994): 81–82.
Please note that this answer does not constitute medical advice. It is only meant to summarize published research related to the original claim and limited to the cited sources. Consult your physician about what these results may mean for your health.