Is giving one's bike a human name and/or referring to it as 'he' or 'she' an instance of the
pathetic fallacy?
Not unless you are Wordsworth

A closer term is anthropomorphism. Ships have been 'she' since the Anglo-Saxons, after all.
Personally, I don't give names to cars or bikes. I don't think it's wrong, or silly. It just doesn't work for me. Since we got an MX-5 last year, my wife has been trying hard to get us to call it something. Yes, it's cute and quite feminine, but despite suggestions like Matilda and Myfanwy, it's still 'the Mazda' to me. The bikes are 'the Dawes', 'the Amazon' and 'the electric bike'. No imagination, I know.