Hi, T -
The version I learned is

Ride a cock horse to Banbury Cross
To see a fine lady upon a white horse;
Rings on her fingers and bells on her toes,
And she shall have music wherever she goes.

The Oxford Dictionary of Nursery Rhymes (Iona & Peter Opie, 1951, 1997) gives this and two other versions, all from the 18th century. They note that some versions describe the lady as old and the horse as black, and the destination as Coventry Cross.
Here are the other versions:

Ride a cock horse to Banbury Cross
To buy little Johnny a galloping horse;
It trots behind and it ambles before,
And Johnny shall ride till he can ride no more.
    (sung while 'galloping' a baby on the knee)


Ride a cock horse
To Banbury Cross
To see what Tommy can buy;
A penny white loaf,
A penny white cake,
And a two-penny apple pie.

The notes after that third version are fascinating: The pastry cake of Banbury has been renowned for several centuries. 'Banberie cakes' are referred to in 1586. Their ingredients are mixed peel, biscuit crumbs, currants, allspice, eggs, and butter, folded into a circle of puff pastry. And very good they are, too. When in Banbury it was well worth visiting 12 Parson's Street, 'the original Banbury Cake shop,' to try one.
This book is fascinating. I may post more later. No, I gotta do it now....
The Opies guess the song comes from the 15th century, since the cross at Banbury was destroyed at the turn of the 16th century. A Jesuit priest wrote in 1601, "The inhabitants of Banbury being far gone in Puritanism, in a furious zeal tumultuously assailed the Cross that stood in the market place, and so defaced in that they scarcely left one stone standing upon another."
The term cock-horse has always been used to describe a proud, high-spirited horse. To "ride a cock horse" is usually taken to refer to straddling a toy horse (or grown-up's knee) and is found used in this sense since 1540.
It has been suggested that "bells on her toes" points to the 15th century, when a bell was worn on the long tapering toe of each shoe.
-Joe Offer-