In my experience British people would almost always say "I like to cycle," or "I like to go cycling," or "I like to ride my bike." It sounds unnatural to use the word "bike" as a verb. Is this an Americanism? (Unless one is discussing motorbikes - in that case a Brit might talk about "going biking" or being "a biker.")
surprised no one answered you! but for any other brits who might want to know the answer, yes in American English to bike is probably the most common way of saying this (well, to ride bikes/a bike is equally as common). If one were to say cycling, which doesn't sound wrong to my ears at all, it might imply they're pretty serious about the athletic activity and have a bunch of gear (other than just a helmet). Or in the past 4 or 5 years, businesses that offer cycling classes have become very popular, so cycling could refer to a stationary bike at a gym-like place.
My answer of "I bike yearningly, unless it rains" was found to be incorrect. Actually, I discovered something quite interesting:
The German "gern" is a cognate to the English "yearn" (with an apparent phonetic shift of /ge/ -- /ja/ sometime in English's past, explaining how the prefix ge- became ya- which then became a-, as in the words asleep, awoke, amiss, etc.). It derives from the Proto-Germanic "gernaz."
I assumed that the Dutch "graag" is a cognate to the German "gern," but indeed it is not! Graag derives from the Proto-Germanic grēdagaz, meaning "hungry." (Probabily in the same sense that one would say that one "hungers for battle," or one "voraciously read a book," with voracious being a Latinate synonym for "hungry.") The English "glad," though, derives from Proto-Germanic "gladaz," meaning "shiny, radiant," and so on.
tl;dr: Graag is NOT a cognate to yearn. Graag is NOT a cognate to gern. Gern IS a cognate to yearn. Graag is NOT a cognate to glad.
As bike is often used for motorcycle, and simply because it "just is", in British English "I like to cycle" is correct and commonly used. If I say "i bike to work" it will be uncertain if I mean pedal cycle (fiets) or motorcycle (motor). Also the speech emphasis is surely wrong on "regent". Surely the pronunciation should either be "régent" or have stress on neither syllable in this case? Not regènt, surely?