Also here in the US. But it can refer to either a bicycle (non-motorized) or a motorcyle (technically, also a bicycle if it has two wheels). Context tells you which one it means. Like you could say my bike is a Schwinn or my bike is a Harley-Davidson.
I don't quite understand the logic of this sentence and several similar ones that I have seen. My logic would be to say "This is my old bike" or else "This was my bike". If you say "This was my old bike", what is it now?