Translation:Yes, I am able to cycle well with my mother.
I'm trying to decide whether I like any of "cycle" or "bicycle" or "bike" as a verb for "to ride a bicycle". I think "cycle" is the most alien to my idiolect, of the three.
I think by default I'd say "He biked up the hill." If someone said "He bicycled up the hill," that would make sense but sound a bit unnatural. For "He cycled up the hill," unless there was context to establish it, I would genuinely have to compare a number of definitions of the word "cycle" before eventually deciding that it was probably about bicycles.
Where are you from? I've always used the verb to cycle. There is also a National Cycling Network here in the uk http://www.sustrans.org.uk/ncn/map/national-cycle-network/about-network
I power cycle computers. (Put them through the cycle of powering down and up.)
I cycle through a set of options. (Iterate through them using some specific selection indicator.)
Both of those meanings of "cycle", as a verb, come to mind before "ride a bicycle". If I don't have context to suggest bicycles, it doesn't come to mind quickly. And if I do have context to suggest bicycles, the whole exchange suddenly sounds Very British.