[Alice, my superior, doesn't agree. She whirls round, her blue eyes flashing.
"Lucinda, are you winding me up?"
She calls me 'Lucinda' when she's annoyed. She's having a go at my humming.]

Be careful to not tell rather than show. You state twice that Alice doesn't like Lucinda's humming. Your readers can get that from the way she reacts and how she talks, you don't need to say it again as if they're dull.