The tiny types of bumps like in your picture are usually small clogged pores (comedones). They're basically a non-inflamed type of acne.
The best treatments for it are Rx-only (Retin-A Micro, Tazorac, Differin, etc). In the meantime a face wash with salicylic acid in it could help, like St. Ives Blemish Control Apricot Scrub.
Let me know if that helps!