1 I can ride a bike - I have learnt how to ride. 2 I can ride the bike - I can ride the specific bike. 3 I came here today by bike / on my bike / on the bike. 4 I brought my bike / the bike. I think you are asking about 3; Without 'the' is always good, a safe.choice. Your reasoning about 'the bike' is very good, but I would rarely use it. Oddly, the equivalents 'the car', 'the bus' and 'the train' are all much more widely acceptable. Buses and trains are scheduled services, this gives them a more established and 'known' status - they need no introdiction. But what about cars? Perhaps there is an assumption that 'everybody has a car' whereas cycling is somehow less universally accepted as a means of transport - I know this because I cycle a lot, and people think I am crazy to do it. Also the term 'bike' could mean a pedal cycle or motorbike, it somehow has indefiniteness built in. If I were a biker (motorcyclist) wearing my leathers and talking to another such biker, perhaps while drinking with other bikers, I might say 'the bike', as we would have enough shared experience for it to seem natural, but probably only under such conditions: if I met the same person at work the following week I probably wouldn't. Maybe this is because my friend thinks I might own several bikes, and they don't know which one I rode to work.