That's pretty much all there is of it, though I remember the third line as "The King of Spain's daughter".  Iona and Peter Opie, in The Oxford Book of Nursery Rhymes (1951), give a further couplet:

I skipped over water, I danced over sea
And all the birds in the air couldn't catch me.

I seem to remember that from "Listen With Mother" back in the '50s, and certainly still recall a tune; substantially the same as the one Jon gives.  The Opies comment:

"Edith Sitwell in Fanfare for Elizabeth (1946) pictures Lady Bryane, governess-in-ordinary to the young Princess Mary and then to Elizabeth, singing this song to her charges, and remembering a black and terrible shadow, the shadow of Juana of Castille the mad "King of Spain's Daughter", who visited the court of Henry VII in 1506.  This picture was probably inspired by James Orchard Halliwell's suggestion* that Juana of Castille is here celebrated.  Whether there are grounds for the theory is not clear.  The rhyme is said to be the favourite recitation of the Shakespearian actress Dame Sybil Thorndike"

*in The Nursery Rhymes of England, 1853.

Malcolm