I've heard from 10-20 minutes for each cycle.
A good rule of thumb is to pump the volume of your fish tank 1 time per hour. This will allow enough filtration to occur to keep your water quality high. Since the volume of grow bed is 1/2 that of the fish tank it also means that your grow bed filtration will only support 1/2 the density of fish that a 1:1 ratio would. You will not need a whole lot of fish to grow a lot of plants - something in the range of 3-8 pounds. My system has a grow bed 1/2 the size (24 Gallons) of your total and I only need 2 adult goldfish to power it or something like 1.5 pounds of fish.
Once you put the media in the 1/2 drums it should only take about 15-20 gallons to cycle both grow beds so you would need to cycle 5-7 times an hour to meet the rule of thumb guidelines of pumping the volume of your fish tank 1 time per hour. If you add another set of grow beds (which would match your fish tank) you would only need to cycle 3-4 times an hour.
until you start seeing nitrates. add some aquarium water like 4-6 gallons to speed it up.