Are Bjornaer ancestor spirits related to blood inheritence?
Some forms of Mythic Blood represent descent from a supernatural creature, such as a Dragon.
Since Bjornaer cannot have a HeartBeast of Might, does that mean that a Bjornaer can't have certain Mythic Blood types?
No, why would it?
Bjornaer magi can have all the types of Mythic Blood that other magi can have. No ancestor spirits need to have been involved - even if they are literal ancestors, a given person has lots of ancestors of all sorts if you go back far enough.
Note also that if they do have Mythic Blood it does not need to have any connection whatsoever with their Heartbeast.
I also don't read ancestor spirits as being ancestor spirits of a given individual. They are ancestor spirits of a clan or house, magically speaking. Although there may be some blood desccent in the Bjornaer, and indeed there are unique mythic blood lineage suggested for the House, fundamentally there is nothing in the House that forces an individual to be descended from anything. The only prerequisite is the Gift, and you are mystically connected to ancestor spirits mostly by sharing in the mystery rites and tradition of the house, not by blood itself.
Occasionally the words used throw my modern mind - Ancestor usually implies "by blood" to my thinking.
So you are suggesting that I need to think Ancestor Spirits like an analogy to the US Founding Fathers - they are the Founding Fathers of all US citizens, even the ones whose families didn't emigrate to the USA till many generations later.
Pretty much that, yes.
But even if the ancestor spirits are actual ancestors by blood (which is not the usual interpretation) they do not constitute all the ancestors of a Bjornaer mage. So a Bjornaer mage can (and will) have plenty of other ancestors as well.
I'm suggesting that, for the average Bjornaer, it's initiation into the Heartbeast form that connects them to "ancestral spirits".