In 1, "each" is an adverb, so doesn't influence the number of "have", right? On the other hand, in 2, "each" is a pronoun, affecting the number of "has".
1.We each have a bike.
2.Each of us has a bike.
I wouldn't call it an adverb, though some analysts might. I don't think it matters. What matters is the meaning:
We ...have [one] bike [each]
Each [individual] of us has a bike.
Make the subject agree in number with the verb, and the 'each' takes care of itself.