A warm (over) shirt - something that you can just throw on. So not very smart usually.
And tough enough to survive being pushed through tight bush.
In NZ - possibly the birthplace of the original bush shirt, the Swannie, there are lots of synthetic clones on offer - Ridgeline, Stoney Creek, as well as a load of small brand garments from farm shops etc, so you can debate whether natural fibre is a key component. However I would say that natural fibre gives it some soul.