I ride a bicycle. Or I ride my bicycle. Or (past tense) I rode your bicycle.
There is a special case when we might say "I am driving the bicycle" or "I drove the bicycle." This is when we allow a second person to come on the same bicycle as we are on. So we say that we are giving that person a ride on the bicycle. In this case, we might say: "I drove the bicycle and he road it." OR "I am driving the bicycle and he is riding it."
And unless in a formal context, we would almost always use the word "bike" instead of bicycle. But it would not be wrong to use bicycle in all contexts. (Unless you are talking about a motorcycle!)