The suggestion above to check historical data to get an idea of the time to peak/ time of concentration, and a get sense of the general storm response time is a good one. There are also empirical methods to relate the catchment slope, runoff coefficient, etc. to the time to peak/ time of concentration, which sounds like what you are looking for. You can find examples of them in the MTO Computational Methods webpage, more localized ones might exist wherever you are located. Look for the section on time to peak, although you may need other definitions in there to determine your inputs to that calculation (such as catchment slope).
Keep in mind that 'runoff time' is not a specific term, and that the 'runoff time' for a full response may be extremely long, as nature tends to follow exponential responses trends with long tails in recession. However, the time to peak and time of concentration are more specific terms with definitions you can find and apply.
In terms of how long to run the simulation, depends again based on what you are doing. For a real storm, there may be subsequest rainfall events before the full response is seen. If you just need the peak, then 2-3x the estimated time to peak from the methods above would likely be fine, depending on how flashy the catchment is. If you are running a hydrologic model of sorts, then run it for a long time to see the full response to check the response hydrograph, and compare that to real data to help validate your model.