The length of time it takes for a coated screen to dry is directly proportional to how dry and warm the room is and how much airflow you have going over the screen. To ensure that the room or drying box (environment) is dry enough, you want to bring in a dehumidifier. The ideal moisture level in your drying environment is between 30-40% humidity. Perfect room temperatures are between 68-85 degrees F (warmer is better). You will also want air movement both over and under the screens that are drying.
This combination of warm, dry air moving over your emulsion will draw out the moisture in the wet emulsion, bringing its water content down to the 30%-40% levels needed for proper exposure and crosslinking of the emulsion.
This will take as long as it takes within the space you have. Example: If you have an enclosed environment with strong air movement and a powerful dehumidifier, you can have screens ready within 20 minutes. If you have them placed in a corner of your screen room with a single fan improperly placed, it can take several hours for the screens to become dry enough.
Side note: For those shops in humid environments like in the Southern U.S. states, you will have more considerable difficulties creating a low humidity environment. You will find your dehumidifiers fill up with water very quickly, necessitating a drainage tube to ensure uninterrupted operation.