Richie, where did you get the version you posted? It doesn't jive with the version in the link Masato provided, and that's supposed to be the same source. I'd sure like to know the source of the "For the flowers tell me so" line, but I'm not ready to believe you that it came from Warner.

Here's the text from Masato's link:

JESUS LOVES ME
(Anna Bartlett Warner, melody and chorus by William B. Bradbury)

Jesus loves me—this I know,
For the Bible tells me so:
Little ones to him belong,—
They are weak, but he is strong.

CHORUS:
Yes, Jesus loves me!
Yes, Jesus loves me!
Yes, Jesus loves me!
The Bible tells me so.

Jesus loves me,—he who died
Heaven's gate to open wide;
He will wash away my sin,
Let his little child come in.

Jesus loves me—loves me still,
Though I'm very weak and ill;
From his shining throne on high
Comes to watch me where I lie.

Jesus loves me,—he will stay
Close beside me all the way.
Then his little child will take
Up to heaven for his dear sake.

Source: Say and Seal, vol. 2, 1860, pp. 115-16, by Susan Warner.

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Note: I did not find anything in Say and Seal that definitely attributes the song to Anna Bartlett Warner. I'm taking that from other sources.
Here's what I found in 101 Hymn Stories, by Kenneth W. Osbeck (Kregel Publications, pp 135-136):

Without doubt the hymn that has influenced children for Christ more than any other is this simply stated one, written in 1860 by Anna Bartlett Warner (1820-1915). Miss Warner wrote this text in collaboration with her sister Susan as part of one of the best-selling novels of that day, a novel written by Susan titled Say and Seal. Today few remember the plot of that novel, which stirred the hearts of many readers. But the simple poem spoken by one of the characters, Mr. Linden, as he comforts Johnny Fax, a dying child, still remains the favorite hymn of children around the world to this day....Dr. William B. Bradbury, the composer of the music for the text, was one of the important contributors to the development of early gospel hymnody in this country.....Bradbury composed the music for "Jesus Loves Me" in 1861 especially for Anna Warner's text and personally added the chorus to the four stanzas. It appeared in its present form in 1862 in his hymnal publication, The Golden Shower.
Other hymns by William B. Bradbury include "He Leadeth Me" and :Just As I Am."

Bradbury's chorus is:

Yes, Jesus loves me!
Yes, Jesus loves me!
Yes, Jesus loves me!
The Bible tells me so.