According to HowStuffWorks, bumps on the scalp are called scalp acne. Scalp acne occurs when the pores on the scalp are blocked by oil and hair products.
HowStuffWorks recommends using salicylic acid instead of benzoyl peroxide on scalp acne to avoid bleaching hair. Salicylic acid exfoliates the scalp to remove dead skin cells that cause clogged pores, and can often be found in dandruff and medicated shampoos. Tea tree oil in its pure form or as an ingredient in a shampoo is an effective preventative and spot treatment. Antibiotics or a prescription-strength topical medication may be needed if scalp acne is resistant to over-the-counter methods.