"Could a Bishop move from d1 to e8 along the path d1-c2-b3-a4/4-b5-c6-d7-e8?" (a4/4 is a typo, h5/5 is correct)
No, a4/4 is not a typo. It is sandwiched between b3 and b5, and h5/5 is on the other side of the board from these spaces.
Yes, that is possible, but only in two moves.
Okay, but here's what you wrote previously:
"In this diagram, it looks like the Bishop can move from b5 to b3 or from g4 to g6. Is that a correct interpretation?" Yes, that is the correct interpretation.
To be clear, my questions were about what a Bishop could do on a single move. If the longer move I described cannot be done as a single move, then I would presume that B b5-b3 is illegal for similar reasons. Or is there some asymmetry that allows one and forbids the other? I should ask, could either "B b4-b3" or "B b3-b5" ever count as a legal move?
No, a4/4 is not a typo. It is sandwiched between b3 and b5, and h5/5 is on the other side of the board from these spaces.
Okay, but here's what you wrote previously:
To be clear, my questions were about what a Bishop could do on a single move. If the longer move I described cannot be done as a single move, then I would presume that B b5-b3 is illegal for similar reasons. Or is there some asymmetry that allows one and forbids the other? I should ask, could either "B b4-b3" or "B b3-b5" ever count as a legal move?