There is a waterproof cast available these days, but it costs extra. When I broke my foot last year, I got the "regular" cast b/c it was a workers' comp case, & I knew they wouldn't go for the extra.
We bought a box of large trash bags just to use for the cast (I had it for 2 wks) and used 2 for each shower. The first one got put on & tucked into the top of the cast. The second one went over it & was rubber-banded closed (we used 2 rubber bands). It wasn't foolproof (there were occasional minor leaks) but overall it worked well.
I also broke my right arm as a kid (am right handed) when I was 10. They put a kind of splint cast on it. It was a bunch of plaster strips inside one of those sock thingies, molded to the back of my arm. A big ace bandage was used to hold it in place. That meant I could take it off at bathtime. I don't recall having much difficulty doing things with it on, but that was nearly 30 years ago
I also broke my left wrist the following year, & had a hard cast for that. Mom wasn't sure where I got the klutzy gene from. :rofling: