"I had trouble finding general rules of thumb on what a "safe" discharge time is. Any ideas?"
There are no general rules of thumbs, because the safe voltage and time really depends on the system at hand and what kind of troubles you are defending against.
This is a system engineering risk analysis problem, in general, not a purely electronics one.
If for "safe" you mean "safe for human operators to touch the circuit", you should guarantee that the voltage in any part of the circuit goes below a human-safe threshold in the time interval between the actuation of the power-down switch (or whatever other mechanism is used to power-down the thing) and the instant the circuit can actually be physically accessed by an operator.
So this may require some real-world simulation/assessment/guessing about how quickly an operator can open the chassis and access the circuit in the worst (i.e. quickest) scenario.
For high-safety environments, you may also want to design-in some kind of interlock between the power supply and the panel that allows accessing the circuit, so that no operator can even open the panel unless the circuit is safe to operate upon.
Defining a human-safe threshold voltage is a bit tricky. Usually 40V DC is considered safe for the risk of electrocution in normal conditions (i.e. the contact with the human body happens in a dry environment, with the operator's skin intact).
This is a relevant thread on this site.
This doesn't take into consideration other risks, e.g. sparks caused by mishandling the circuit that can induce fires in the system.
You may want to read this Wikipedia Article for general guidance, and then consult more thorough safety guidelines sources.
If you want to be sure, go for a <2V threshold. Or less than 1V if feasible by your bleeding circuit.
Once you choose the voltage threshold, it's a simple exponential decay with good approximation (if the bleeding circuit is complex and non-linear you may need to consider the switching time of your active parts).
Keep in mind that if the bleeding circuit is not a simple resistor, you may have some trouble determining the "time constant". Therefore apply generous tolerance margins. Anyway, once you determine you need to reach safe voltage in, say, 5 seconds, design your circuit to reach that voltage in half that time, or even less (don't taunt Murphy).
Note that if your caps need to be discharged because of some kind of emergency shutdown (e.g. water ingress detected in the plant), you may want to VERY CAREFULLY estimate how quickly the problem that caused the shutdown is going to "reach" the circuit and causes troubles.
You may also need to design-in some emergency discharge mechanism, perhaps using sacrificial components that will dissipate the stored energy and get "fried" SAFELY in the process (remember Fukushima: the emergency generators where themselves damaged, thus the energy of the core had nowhere SAFE to go).
BTW, don't think that discharging some stored electrical energy can be done in however small time you would need. Generating a very short, high-energy, electrical pulse can generate a lot of EMI (Electro-Magnetic Interference). This pulse could propagate as an EM wave or as a conducted electrical pulse and could wreak havoc in sensitive control circuitry nearby (e.g. an MCU control board).
If you don't take appropriate countermeasures (e.g. lengthening the pulse and/or smoothing its edges) when your bleeding circuit kicks-in, it could cause failures in other parts of the system, and you may be dealing with a chain-reaction of failures.
