I have to admit that I had no idea about the bloodline until about a year ago and I agree with you I think that probably half the population of G.B. and the USA has it!
I think that the Battle of Bosworth was tragic as I am a bit of a Richard III fan. Which side was your family on? If you were on the side of the Welsh upstart Henry I promise not to hold it against you - well not much anyway:-)
The one thing that has convinced me that we are related though above all else is the eccentricity factor. That most definitley runs in families:-)