As someone who spends a lot of time on my bike on the road I can tell you that typically children & casual cyclists who are out to get fresh air or see their neighborhood are "bike riding" or "riding a bike" whereas people that pursue the sport and try to maintain a hard pace are "cycling".

Both are find sentences.  Another way write it would be like this:

"I like bike riding."  or   "I like cycling."  or   "I enjoy cycling."

Funnily enough, "biker" also conjures up someone on a motorcycle for me. We tend to use "cyclist" for people who ride bicycles.

We have a similar government initiative in the UK, only its called the 'cycle to work' scheme instead. It appears there may be regional differences in how the words are interpreted.

Personally, if someone told me that they were a biker or that they like biking, it conjures up images in my mind of Harley Davidsons and Hell's Angels. Perhaps I watched Easy Rider too many times :)

I don't see anything wrong with "I like biking." My husband bikes(as in rides a bicycle) to work and I've never had an issue with someone misunderstanding and thinking he rides a motor bike. Our county has a "Bike to Work" promotion which refers to bicycles. Maybe it 's a regional usage, but here if you say you like biking, I think most people will assume you're referring to a bicycle. "I like riding a bike" and "I like cycling" are also fine.n