Found it - the instrumental intro song for Big Jon and Sparkie was "Teddy Bear's Picnic" performed by Ethel Smith.

It exists as a 78 and is on several 33 1/3 albums of hers as well. May have been issued later on a 45, too.

It is easy to find, most online stores have Ethel's greatest hits CD which contains it.

(Thanks for the info, Dan C.!!!)