You’re taking the world possession much to literal.
The word possession not only refers to physical control but the ability to take control whenever you want. If the two are passing it back and forth and can just stick their hand out and get the bowl, both have possession in terms of the law, regardless of who is physically holding it.
From my first year law book:
Possession is defined as "The detention or enjoyment of a thing
which a man holds or exercises by himself or with others, who keep or exercises
it in his name.
In order to complete a possession one must have the actual intent to possess. (In other words if someone throws and object at you and out of reflex you catch it, you are NOT in possession)
Possession may be accomplished by taking, occupying (as in a house), detaining (like an arrest or a security guard), or cultivating (as in a farm).
Possession is constructive when one holds legal title, or actual when one occupies or uses. (In this example you hold legal title to your car so you possess it, but a theif steals it, so he has actual use. In this case you BOTH have possession. Of course, while the thief has possession he is violating lots of other laws).
Abandonment forfeits the right to possession. (If you leave your house, take your belongings, don’t pick up your mail, don’t pay taxes on it, etc… It can be considered abandoned and you don’t have possession. Title to the property is covered by other laws)
Possession is lost only when the transfer of object is with the intent to diverst himself of the object. (In the OP example since the bowl was going back and forth neither possessor had the intention to divest himself but simply surrender custody of it temporarily)