Sorry to hear that you are having this sort of problem and I am disappointed that your GP has not given you an adequate explanation for your bleeding. Bleeding can be caused by a whole host of different things, so it is best to have a medic investigate it and give you an acceptable explanation. If you don't get that, then I suggest you ask for a second or third opinion. If the bleeding is not serious then at least you will have peace of mind, which is very important in these matters.
I occasionally have bleeding from my anus but it usually stops in a day or two. If you are irrigating, then it could be that you have slightly damaged the tissue either internally or, more likely just at the entrance. These minor lesions soon heal up on their own. However, it is as well to identify what has (or may have) caused them, as you might be repeating the problem. Sometimes the irrigation tools /catheters get very slightly snagged and those snags can be sharp enough to do damage. Also, it is always a good idea to make sure your fingernails and cutical skin are well and smoothly manicured. The smallest of tears can cause quite a lot of blood.
Also, I find that the colour of the blood will give me some clue as to where the damage might have occcured, If it is bright red, then often the damage will be near the external surface ( I can usually confirm this by using a soft tissue to dab the areas where I think it might be). If the blood is darker or globby, then it is more likely to have been internal and there for some time before coming out. These incidents seem more concerning because they could mean something more serious than simple surface damage. I sometimes suffer from an anal prolapse which is not always noticeable as it can go back in on its own. However, damage can easily be caused by the soft tissue being abrased by clothing, and if it then disappears back into the body, I woud not know what was causing the trouble, if I had not identified it as having happened before.
Like I say, these problems need to be properly identified by someone who knows what to look for. I saw one or two doctors who said there was nothing wrong- then I met one who asked me to squat - standing on the rim of the toilet so that he could get a better look. He immediately diagnosed a prolapse, which would only be noticeable in this squatting position (which incidentally is also the sitttng position). When I simply laid down for an examination it hadn't showed up and when I stood up, it went back in. I was simply glad that I had found a doctor that knew what to look for and how to find it. The explanation made perfect sense and now I can take precautions based on some sensible advice.
I hope you find a solution soon as these 'bloody' problems can be quite worrysome.