I would think an old tent pole would be your best bet because then it would break down into smaller lengths. A 1/4 inch fiber glass or aluminum tent pole would be about right.

I think you can get a 1/4" fiberglass pole made to your specs for $10-15 at https://tentpoletechnologies.com/

Shipping might double the cost

I bought one from them once for a cheap Ikea kids tent. My kids loved the tent but destroyed the plastic poles it came with in a week. I was very happy with the poles I got. They lasted longer than the tent.

An old fishing pole would give your tent an asymmetric curve as the handle is much stiffer than the tip. A fiberglass strip might be more flexible than a rod, but I can't think of a good cheap source plus packing it would be difficult.

If you want a nice hemisphere shape, the length of the pole is 1.57 (pi/2) times the width of the bivy.