Biked is perfectly normal American unless you grew up in Minneapolis. It definitely looks more of a serious activity than going for a bike ride. Cycled would be much considered formal in AE while BE and usually the internationals learn the verb by cycling. I would rather use cycle for climate oscillations or economic ebb and flows.
I agree that 'we almost never bike' is an accurate translation for 'wij fietsen bijna nooit'. However, 'we almost never bike' is not necessarily an accurate translation of 'wij fietsen bijna nooit'.
As can be read in the link you provided 'Danny bikes to the park and back every day' means 'Ride a bicycle or motorcycle.'
According to this link (https://en.oxforddictionaries.com/definition/bicycle) 'we almost never bicycle' could be an accurate translation also.
Edited (since i can't reply to your reply anymore). From Dutch to English: ‘wij fietsen bijna nooit’ is an accurate translation for ‘we almost never bike’. According to your link, fietsen is an accurate translation of the verb ‘to bike’.
From English to Dutch: ‘we almost never bike’ is not necessarily the most sound translation of ‘wij fietsen bijna nooit’ since it’s not clear whether it’s used to indicate a bike or motorcyle. I stand correct, I should have said ‘not necessarily the most sound’ instead of ‘not necessarily an accurate translation’.
Maybe it's just my colloquial usage as a native speaker, but the sentence "we never bike" is just simply not used/sounds strange. "I never bike to work", for example, also sounds funny. "I never ride my bike to work" would be a more correct colloquial context, so the only direct translation for this sentence for me would be "we never go biking". I understand your translation, but for normal usage, that's where I stand.