It's incorrect to state that hospitals don't use plaster nowadays to set broken joints. They still do for some joints but it depends on the type of fracture involved.
Baycast is a polyester cotton bandage which is impregnated with water activated pre-polymer resins and it does indeed set hard in around 20 minutes or so. Baycast is a registered trademark of Bayer AG and is an innovative product but it's lack of porosity needs to be carefully evaluated before it's used. There is a version of Baycast available for use by veterinary surgeons and this has the name Vetcast.
Now for the bad news. Baycast is one of the many products used in A&E departments that have a closed supply chain. These products go from manufacturer to wholesale hospital supplier and into hospitals with no other company involved. Because of this, they are not listed in the BNF, are not held in stock by community pharmacists and cannot be prescribed by community physicians. This results in these products being virtually impossible to obtain outside a hospital. The same applies to similar products such as
Dynacast XR.
When I read your question earlier, it struck me that Baycast could have some dubious uses too outside a hospital so I checked with a A&E consultant in my uni's medical school. As I suspected, the sale of Baycast is restricted to hospitals, vets, some GP surgeries and some sports injury specialists. It's also very expensive.
If you have a genuine use for it, I'd suggest you have a chat with your local vet.