It is important and helpful to know whether the shift is happening on the old bow or the new bow, but how does one decide which one is appropriate for a certain situation–Why is one shift on the old bow and another on the new bow?

In general it is a question of taste whether you shift on the old or the new bow. Sometimes you would like to shift even between the two, if you want to make an unhearable shift. If you like to produce a clearly hearable, expressive slide, you should slide on the new bow.

Singing is an extremely good advisor actually. Just sing the passage you want to play on the instrument and watch carefully how you connect the notes intuitively. Are you going into them? Do you breath before a new note? After analyzing it try to imitate you singing on your cello. Also watch great singers and analyze their “Shifting”.