Possibility of Naegleria Fowleri growth in a bucket full of water in my bath tub for a month

Question

I have a bucket at the end in my bath tub. It is always full of water by collecting it when I shower. I would assume it has been like that for a month and I didn't drain it. Today when I was bathing a little splash of it went into my nose. I have heard that in a bucket of water, chlorine disappears within a day and the water I use to shower is warm. Agreed, the temperature of the bucket water might have come down but still it would have been a little warm. I am worried that within this month Naegleria Fowleri could have grown in it and I am worried about the infection due to the splash. Please help me with an answer. I am from New Jersey.