wind-blown dust falling like rain
霾 centers on wind-blown dust or fine particles that fall like rain, creating a hazy, dusty atmosphere.
霾 combines 雨 (rain) with 貍, which likely contributes the sound and the idea of something covering or burying, together suggesting dust falling like rain.
Rain 雨 falls from the sky, but instead of water, the lower part 貍 (which looks like a creature buried in dust) shows it's dust and particles raining down.
For バイ, imagine buying a mask to protect yourself from the dusty rain: buy -> バイ, and the mask keeps the wind-blown dust out.