About how much would it cost to have a shower build in my half bath in my basement?

That's a bit like asking how much a car is. :-)

The answer is , it depends.

It depends on the quality of fixtures and finishings, where the plumbing is now, if there is capacity on the plumbing to add more fixtures, and if you're doing it yourself or hiring someone to do it.

As a rough guess, $1,000 to $10,000 should be the price range. If you are serious, quotes are free, so think about what you want, and then have a few contractors in if you are not going to do it yourself.