Common ground between a current source and a power supply
The output of the 9V adapter is floating.  The output of the bench-top power supply is probably floating too.  If at least one of them is floating, then you can connect grounds grounds with a wire.  The current through the wire will be negligible.

Whether or not connecting the grounds would cause noise issues depends on the nature of the device.  If it generates EMI, then be prepared to deal with it (that would be a subject for a separate question, and similar questions have been asked on EE.SE).

On a different note, your current-sense inputs are wired wrong.  If RS+ and RS- are tied together, then the current sense amplifier will always read 0 (zero).  RS- should be connected to the low side of the current sense resistor (maybe via a Kelvin connection).