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The point you have raised about cycling and warm humid environment do have a logic of causing fungal infection
but fungal infection rarely causes bleeding. The bleeding can be due to other several cause that can be external or internal. the external cause can be simple skin tears or cracks.
The internal causes which are the most common for anal bleeding can be hemorrhoids, Irritable bowel syndrome
, malignancies on infections, Therefore it is recommended to visit a doctor and have a proctoscopy for the evaluation of bleeding.