differential opamp reference
It's an over-simplified model for the purposes of your question.

Yes, each transistor needs an input bias current, and there needs to be a path through the external circuit for that current. So the differential voltage source can't be truly floating with respect to the power supply.

Some opamps have extremely low input bias currents (a few nanoamps or even less), and a very large resistor (10s of megohms or more) is sufficient to supply the bias current.