Discharge rate of a motor run capacitor?
If it's installed in the motor, then it discharges in a fraction of a second, when the power is turned off.
Here is a circuit diagram from researchgate:

You can see the run capacitor is shorted out by the motor coils.
If the capacitor is out of the circuit, it will effectively never discharge itself. The polypropylene capacitors used for motors have such low leakage they can remain charged for months
Also, in my experience, they can charge themselves from static electricity, so if you find one on the shelf or buy a new one, it might give a nice spark when shorted, or bite your fingers.
You're right to avoid using a screwdriver - it damages the screwdriver and probably the capacitor too. To safely discharge it you need a high value resistor, 100 kOhm should do. 30 microFarad and 100 kOhm will discharge most of the way in 10 seconds. You could also improvise with a wet rag or a green twig from a tree, give it several seconds, then short circuit to be sure.
In most electronic products large high voltage capacitors will have bleeder resistors permanently installed, to safely discharge them when the power is off. I haven't seen these in small motor capacitors. Perhaps because the motor discharges them anyway. Don't install your own bleeder without first learning about high voltage resistors, the common 1/4 W type are ok for a once off discharge but are not rated for hundreds of volts.