I was listening to Ghost Of A Rose by Blackmore's Night, so blame this idea on that song.
White roses are Melody's favorite flower. One day while in the Truffula Valley, she spots a White Rose growing, and absently mentioned her love for them.
From that point on, every time Once-ler saw a white rose, he was reminded of his friend.
And he began to notice small things, too. Like how she always wore a white rose in her hair, or how whenever they would pass by one, she would pick it, despite the comments from The Lorax.
So one day, he and Melody went out and planted a small rose garden by his house Er, tent. Melody spent a lot of her time tending to the roses when things began to get bad. She did all she could to keep the roses alive, but like the rest of the forest and the land, they died.
And after everything has happened and Melody dies, after Ted plants the seed, after The Lorax returns, the garden grows back.
Once-ler spends every day watering the rose garden as well as the trees, and he even talks to the bed of roses sometimes, calling it by the name of his oldest, dearest friend, who died trying to help him.
Melody and the roses are sort of symbolistic of her relationship with Once-ler, because she cares for them so much, and does all she can for them, but they die anyway. She spends so much time caring for him and trying to express her love and gratitude for him, but she never tells him that she loves him. Their relationship dies anyway.
When you see,
A white rose,
You'll think of me.
I love you so.
Never let go.
I will be
Your ghost of a rose.