My mother's first reaction: "Ayumi sings like a bee!"
Nonetheless she seems to really like her, as she thinks her PVs are very interesting and deep. She loves her fashion sense. When she sees Ayu-ish nails or an Ayu-ish dress she's like "OMG it's something Ayumi would wear!".
My non-anime fans friends' first reaction: "She sings like a duck but she looks nice. " They also think she's Chinese
My anime fans friends think of her as an "Inuyasha singer with bad songs" which is totally wrong.
Then again, they only heard "Dearest" and "no more words" so it's not surprising. I don't like those 2 songs much myself.