well i would split it into multiple parts of software first we have genetics which are the building data structure which is compatible with the biological interfaces to reproduce certain features but it's mainly information so this blueprint is why I would have the analogy of it to be software.
So there are certain events how the existing DNA you already have changes in different ways based on non genetic alterations "environmental factors". it's called epigenetics than there is the "miracle of birth" which is basically a merge of the different genepairs which can be as for eye colors be a sort of "boolean" pairs and others are more complex like "how does the lounge work" as well as the brain functions -> are you smarter ? tougher ? higher chance of getting drug addicted and so on.
The reason why I put this first is because now the nature of bugs can be different and the question in nature of the difference between bug, feature, refactoring or old useless feature (apendix)
i am neither a biologist nor a biochemist nor a geneticist nor a psychologist so this is crude and just an idea of how to abstract my thoughts
We have "genetic bugs" for example the downsyndrom, certain inherited diseases where you have to be unlucky enough that 2 healthy parents have a genetic code that via the merge replaces the "wrong" parts and you have a rare disease.
so we could call them "core logic bugs" because basically those things should not fail.
than we have the epi-genetic bugs which are as mentioned environmental and are more or less transferred to your genetics but you did not necessarily inherit them or maybe you just inherited a higher chance to develop them like schizophrenia or depression and so on.
They don't have to break out often even skip one generation but still they remain in the "core code" and can be triggered by the environment also they can be healed in some cases. We still know little about them.
Another nice feature are psychological bugs like the confirmation bias or other prehistoric remnants of behavior in the modern society where the immanent death is more important than the future death ... which is just inherit to human nature.
I can go on :D but I already overlapped several fields with my personal narrative and I personally love @hipkiss91 answer ;D ... which is a "to the point" answer rather than my ... blabla complex system blablaba so many differten types of bugs blablabla :)