The tradition of trying to avoid bleeding on the day one communes is that the body and blood of Christ sanctifies our entire body, since the blood is the life of man (gen 4.10-11) when it is nourished by the blood of Christ it takes on properties of the deified life.. So we treat that which is sacred in a dignified manner . Likewise if the Communion cup is accidentally knocked over it will be wiped up with linens, perhaps using alcohol and the linens will be burned or whatever other appropriate means of discarding that which is holy.
Now the canons dealing with menstruation come from Alexandrian bishops as this was the observed custom in the Alexandrian church. From what I understand this practice is still strictly observed amongst the Copts.
Canon 2 of St Dionysios of Alexandria 260 AD:
2. Concerning menstruous women, whether they ought to enter the temple of God while in such a state, I think it superfluous even to put the question. For, I opine, not even they themselves, being faithful and pious, would dare when in this state either to approach the Holy Table or to touch the body and blood of Christ. For not even the woman with a twelve years issue would come into actual contact with Him, but only with the edge of His garment, to be cured. There is no objection to ones praying no matter how he may be or to ones remembering the Lord at any time and in any state whatever, and petitioning to receive help; but if one is not wholly clean both in soul and in body, he shall be prevented from coming up to the Holies of Holies.
Canon 7 of Timothy of Alexandria 380 AD:
Question: If a woman finds herself in the plight peculiar to her sex, ought she to come to the Mysteries on that day, or not?
Answer: She ought not to do so, until she has been purified.
Theres also the epistle of two great saints of the Church which corresponded with each other on this issue. That is Pope St. Gregory the Great writing to St Augustine of Canterbury:
A woman should not be forbidden to go to church. After all, she suffers this involuntarily. She cannot be blamed for that superfluous matter that nature excretes
She is also not to be forbidden to receive Holy Communion at this time. If, however, a woman does not dare to receive, for great trepidation, she should be praised. But if she does receive she should not be judged. Pious people see sin even there, where there is none. Now one often performs innocently that which originates in a sin: when we feel hunger, this occurs innocently. Yet the fact that we experience hunger is the fault of the first man. The menstrual period is no sin; it is, in fact, a purely natural process. But the fact that nature is thus disturbed, that it appears stained even against human will this is the result of a sin
So if a pious woman reflects upon these things and wishes not to approach communion, she is to be praised. But again, if she wants to live religiously and receive communion out of love, one should not stop her.