I can't speak with certainty about 15th-century England, but I'd like to bring up a few distinct possibilities, prompted by ways in which "modern" societies deal with this problem. Both Jews and Muslims consider it unclean/improper to copulate with a woman who is menstruating. There have arisen, over the years, a number of strategies for dealing with this, especially as relates to the expectation that newlyweds will consummate their marriage vows immediately after the wedding party.

Option 1: Schedule around it in advance.
This requires a certain amount of biological regularity, so I'm not too clear on if this actually was used in the real world, although I've certainly heard of people (supposedly) attempting it.

Option 2: Delay the big day, by hook or by crook
This option is a realistic proposition more often than you might think. For one, events were not planned as exactly in those days, especially if the wedding needed to be held outdoors and therefore required waiting for a few days of decent weather. More often was for the bride to claim a sudden illness a few days before the wedding, the claim being supported by her female relatives or servants. This was easier to do in the days before modern medicine, especially since back then it was less likely that a woman would allow a doctor to examine her closely. Since it was certainly inauspicious to have the wedding with the bride feeling unwell, it was a simple matter (relatively) to wait a few days. Again, sudden illnesses were taken for granted, but also understood to be potentially life-threatening in a way that they don't seem today because of vaccines, antibiotics, etc.

Option 3: Hand-wash gently in warm water. Allow to air-dry.
This option is simple, although I admit I've only heard hearsay of modern brides from conservative Jewish or Muslim families doing this. Essentially, the bride douches herself carefully before the wedding, hopes that nothing comes out, or maybe does a little cleanup before the consummation if at all possible, and then pretends that her "maidenhood" is really bleeding quite profusely, but she feels fine. This is easier than it sounds especially if the new husband has a poor grasp of female physiology. Historical and modern sources support the idea that, in the absence of sex ed or medical training, unmarried young men often have a fairly vague grasp of certain aspects of human biology, which gives the bride a bit of wiggle room.

And, in modern times:
Option 4: Better living through chemistry
In more recent decades, some Orthodox Jewish brides will take hormonal birth control of some sort for a month or two before the wedding. I've never actually heard of Muslims doing this, but I suppose that anything's possible. This is (sort-of) condoned by the Jewish religious authorities, since the bride's goal is allowing a mitzvah to take place that would otherwise not be possible. I have it on good authority that his does happen in the real world, but am unable to provide sources since it's the sort of thing that you don't discuss in public -- which doesn't prevent rumors behind closed doors.

Finally, please don't ask me for gory detail, I'm male, and I've told you everything that I already know.