It shouldn't do anything until the user has told it where the files should end up. It's an unpackaged program, there is no sane place to put it that doesn't have a high chance of conflicting with something else.
That's only due to a lack of standardization. I think a default install to a vendor-specific directory under /opt is a sane place to put it, and there's a very low chance that would conflict with something else.
But sure, absolutely, an installer should prompt the user for an install location, and I think a default under /opt is probably among the best defaults possible, if we consider installing outside $HOME to be reasonable.
Honestly there should be no install-bs.sh and you just bind everything into the file tree as needed. At least that is how it works on Plan 9 which simplifies a lot of things like path which is just '/bin.'