Miles, my friends drifted of the question slightly so I would like to add a few words. Firstly no experiment this time. We cannot have you tearing your hair out looking for bloodstains. You can see from the diagram that the hair is attached to the blood system so it is very likely that removing it would create a very, very small bleed. This would most likely be contained within the follicle (the follicle is the gland/cavity in which the hair grows) so you will not be able to see it.
Hair also goes through three stages of development. In the first stage it is growing quite fast and this can last for up to 5 years. In the second phase the hair growth is transitionary. It will only last for a couple of months but during that time it loses its blood supply, so pulling it out will not cause bleeding. In the third phase the hair starts to fall out on it’s own. As you are seven years old it is likely that you have all of these phases going on at the same time.
Many thanks Miles – a fascinating question.