Again, as with so many plants, there are several different plants that are called spiderwort, or spider wort. So the first thing would be to get a proper identification, preferably with the scientific name.
For instance, the "spiderwort", of the species "Siderasis", is listed as mildly toxic in some lists for parrots.
On the other hand, the "Tradescantia" species is listed as edible and useful, and the leaves, stems and flowers can be used in many dishes.
The tradescantia btw have 3-petaled flowers, which only bloom for one day each.
Siderasis is more of a houseplant, though, and native to Brazil, so you probably don't have that one in your garden
But it's still very important to have a proper identification of any plants you want to try your bunnies on.
If you do have Tradescantia, it's likely safe to try themon a little bit and see how it goes.