I'm glad that your problem is something that's very common and not life threating.
Bright red blood in stool or on toilet is most commonly caused by hemorrhoids, internal ones. Bleeding may be the only sign of their presence. They lie inside the rectum and you can't see or feel them and they are usually painless because there are few pain sensing nerves there.
Sometimes, internal hemorrhoids can be reason for appearance of dark blood in stool and more excessive bleeding as a complication.
Sitting on the toilet for a prolonged amount of time is always linked to swollen hemorrhoids, although there is no exact explanation for that link. It is best to avoid the practice just in case.
Constipation and forcing stool ( stool that is hard or large ) are causing damage to the tissue that supports the swollen hemorrhoids and are putting extra pressure on the anal sphincter( the muscle that surrounds the anal canal as well as the hemorrhoids ), resulting in swollen and irritated hemorrhoids.
Including a proper amount of fiber in your diet by eating plenty of whole grain foods and fruits and vegetables can lead to soft stool and you won't need to strain and seat for a long time on the toilet.
Also, it's recommended to practice good hygiene of that area( washing with antibacterial soup after every bowel movements, before sleeping and after waking up).
Hope this will be helpful!
Best wishes!
Marija