Why can't you connect the + of a device to one battery and the - to another battery (and have it work)?
If you want that bulb to work then you should have complete circuit which is not there in the diagram you have show
what you are telling is completely possible if circuit is complete as shown below:
What you have drawn isn't a circuit, i.e., there is no closed path for an electric current.
Assume that there is a steady electric current through the bulb. Then, electric charge must be leaving one battery and arriving at the other - one battery is steadily becoming negatively charged and the other is steadily becoming positively charged.
But the increasing electric field from such an arrangement would act to reduce the electric current until it was zero.
Thus, the original assumption that there is a steady electric current is false.