Density alone is a weak parameter. For photons with energy below 200 keV — that is, most of them — the attenuation is proportional to Z^2, so barium with atomic number 56 is four times as attenuating as nickel with atomic number 28, and lead with atomic number 82 is about twice as effective as barium — all of this before you account for density.

I've done a bit of searching for materials myself. Barium is mined as barite (BaSO4) or witherite (BaCO3), not baryta (BaO*xH2O, caustic), and USGS lists the price of barite as $180/t, or $0.20/kg.

You also have a K-edge effect, which prompted me to wonder whether you can easily produce barium zirconate from the respective ores, which are both cheap — BaZrO3 (sg ~5.5) is not currently manufactured (Zircon sand was <$1/kg until a COVID-related shortage). But at this point I decided I was overthinking it.