Cause of voltage drifting

Sources of 60 Hz noise can be detected by a piece of tin foil.
Don't forget connecting it to reliable ground.

Drifting of the bath potential level is also a quite common problem.
If it is minor one, you can try re-chloriding the silver wires for the bath ground and for electrodes.

If drift goes by several hundred mV, then it is not just a chloriding issue.
There must be electrical connection between the dish saline and surrounding metallic devices. This happens after saline overflow and spill.
The ground for the amplifier head stage (bath ground) and that for other electrical devices (device ground) are not exactly the same. If the dish saline was connected to both of these grounds, then there would be a voltage drop (= drift).

The joint between the silver wire and the soldered point can produce a strong voltage when it gets wet just like a voltaic cell. The ground wire often sucks up saline and gets wet. If the saline reach the soldered joints, it will cause a huge drift. Do not use a short silver wire for grounding the dish. Keep them dry all time during e-phys experiment.