Thanks Flick Lives for the really cute video.
In Berlin I see a lot of people riding with their dogs in a basket or carrier.
Mostly basket. Sometimes even a doggie trailer.
When we lived in Manhattan in the 1970s we had a dog (until about a year before we left the city). He was a standard poodle. Not a giant and not tiny.
When we went out on the bike he was always excited, asking to go with us.
We got a large sturdy basket that I mounted securely in front of the handle bars. He loved it. He rode well, and never posed an issue of him maybe falling or jumping out of the basket - he just went along trusting me as long as we were upright.
We only had one incident when a cab came quickly around from out right, pulling right, making a turn right in front of us. I had to brake hard and I hit the cab and fell. Randy just jumped out and sat there watching everything until I called him over to me and put him back in the basket.