Since no one has answered this question I'll give it a go.
I work on a busy surgical unit and have a lot of urological patients who require continuous bladder irrigations post TUPR or TUR or if they come in with hematuria. Your first clue about when to irrigate is in the word "continuous" Essentially, this means that irrigation fluid is constantly streaming into the bladder and exiting via the catheter at a constant flowing rate. You control the rate of the irrigation with the flow-meter wheel until there is a continual flow that flushes blood clots and sangueous drainage along with urine without causing a blockage which would then require manual irrigation (and can require some real strong muscle strength!).
Generally the surgeon will order "Run until CBI clear". But what does "clear" look like? After most uro procedures the output is sanguenous with some blood clots present in the returns. Some nurses believe that once the clots have finished passing - that means "clear" even though the output may still be quite red with some residual tissue or sediment still occasionally passing. Other nurses like the outflow to be at least cranberry to light pink without clots or sediments, in order for it to be "clear". I am somewhere in between.
I generally start reducing the rate of flow once the blood clots have cleared until a nice cranberry colour is obtained. I then reduce further over night to watch the output and drainage quality. I have them mobilize in the morning to watch first passing to see if its too sang or if more clots appear or if its clear. If in MY the drainage is "clear" and the patient is comfortable, I then call the surgeon if they haven't come in to assess their patients to get an order to clamp and d/c the cbi and put to straight drain.