You can use 2 baskets for bicycle.
Stack one over the other.
Tie them together with strings, clips or wire cables at the top of both sides.
You can use a cable ties on one side if you want it to become a permanent cage for your pet.
You can place the fabricated cage horizontally and strap it...
...on the rear carrier of your bicycle.
It is smaller and likely cheaper than the ones you get at the pet shop, especially, if you need only one more basket to fabricate it.
