When you're mad, or a genius, or both, like Syd Barrett, your conventional sense of rhythm flies out the window. "Bike" is mostly in 4/4 time, but with one or two extra beats sprinkled in here and there. Amateurs who try this trick usually make it too obvious, but on "Bike," Barrett is able to insert these extra beats seamlessly and naturally. He doesn't seem to think in 4/4 time, he's just singing freely, as you would if you were humming to yourself walking down the road. Of his contemporaries, only the Beatles have been able to work in these natural time-signature changes, as seen on "All You Need Is Love," "Lucy In The Sky With Diamonds," and "Here Comes The Sun."
The other interesting note about "Bike" is that Syd Barrett sings "You're the kind of girl that fits in with my world" on a slide melody. That means he starts the line on the top note (A) and smoothly descends to the bottom note (D). Since there are more syllables than notes along the way, he actually sings some quarter-tones (notes that are in between consecutive keys, therefore unplayable, on the western keyboard).