Good question. So first of all, we speak of "riding" a bicycle, not "driving". We use "driving" mainly for cars or trucks. Things like that. We "ride" bicycles, scooters and motorcycles.
But to your question. I would say, "Wow, I've never seen a dog riding a bicycle before! That's amazing!"
You could say, "I never have seen..." but "I have never seen" or "I've never seen" is a much more common word order.
Even in North American English, we wouldn't use the simple past for a sentence with "before"
I've never eaten bananas before.
I've eaten plenty of bananas before.
Before now, I've never seen the inside of this building.
(There is an exception if you are using "before" to establish a sequence of events in your story: "Before I came home, I ate dinner at my friends house.")