“I've been humming that song all day.”

You heard a catchy new song a few days ago with your wife that you both liked. Today you were singing the song quietly to yourself while you worked. You want to tell her about this. You say:

I've been humming that song all day.

hum (a song)

To "hum" a song means to make the notes of the song with your mouth closed, without saying the words. People usually do this quietly for their own entertainment.

(someone) has been (doing something) all day

People use this phrase to describe something that they did several times in a day, and that they might continue doing.