Can anyone remember the lyrics / artist / title of this song?

Back in the early-to-mid 1970’s, my little brother had a 45 rpm record, a childrens’ record, I believe, which had a man accompanied by a guitar singing this song:

I had a horse and his name was Bill
and when he ran he wouldn’t stand still
He ran away,
One day,
and also I ran with him.

He ran so fast that he could not stop
He ran right into a barber shop
(something something)
With his eye teeth
in the Barber’s Left shoulder.

The song goes on with lyrics about a girlfriend named Daisy, when she sang the cat went crazy, etc. Does anyone recognize this song? Does anyone know the title or the artist? Even though I am somewhat older than my brother I loved this song too, and would like to find it again.

Thats IT! Thanks!