Four girls with four different names for one, off to find a bird's nest, in a rhyme built for practising names and counting. They leave four eggs behind, so nobody comes away with too much.
From Mother Goose / Nursery Rhymes (traditional). See the whole collection.
Elizabeth, Elspeth, Betsy, and Bess,
They all went together to seek a bird's nest;
They found a bird's nest with five eggs in,
They all took one, and left four in.
About this rhyme
The riddle's arithmetic checks out against the text: if all four names are one girl, only one egg is taken and four remain, matching 'They all took one, and left four in.'
A riddle wearing the costume of a rhyme. Elizabeth, Elspeth, Betsy, and Bess sound like four different girls finding a nest of five eggs, but they are all nicknames for the same one, which is why only one egg goes missing and four are left.
Ask the child how one girl can have four names before you give the answer away.
Public domain. Text from The Real Mother Goose (Blanche Fisher Wright, 1916), via Project Gutenberg. View the source edition