White bathing suits depend more on your skin tone than your hair color. If you have a tanned skin tone, white will look really good. If you have very light skin, though, you may want to switch to a solid color.
Brown hair deff will look good with a white bikini! It should be very cute but if you're more on the pale side then a pink bikini or any warm colors would be cute and a smart choice! If your more on the tanner side or a darker skin tone then a white bikini should be perfect