Aktau, Kazakhstan to Bukhara, Uzbekistan?

I'm currently in Aqtau/Aktau, Kazakhstan. The trains look really tricky to get to Bukhara, and I'm wondering if there's a better way, as currently it looks like going back up the line to Beynou (no choice) at night, waiting until the early morning train from there to Nukus or Kungrad, and then down to Navoi, and then hoping there's a train, bus or taxi from there to Bukhara? The train line doesn't seem to go direct to Bukhara unless you go all the way to Samarkand/Tashkent and route back in?

Any better suggestions appreciated.