Oh come on, 'hack life' & just use bottles (or whatever containers available / practical), and open up windows. It isn't hard.
Bigger issue is time spent (daily average) on getting to a water source, and how clean/safe that water is for drinking. Boiling to kill parasites etc adds more time expense.
Opening a window works for a very small livable part of the Earth. Try opening a window as Pharaoh... yeah, I'd rather have AC. And consistent heat in the winter.
Right up until you hit your first major infectious disease or crippling injury, and have to depend on the medicine of 536 to treat it, and hope the result doesn't make you die before your year is up.
Not to mention: Very easily, accidentally running afoul of some regional religious or social taboo/law in a way that seems banal to you but at the time carries some grotesque variant of the death penalty plus torture, or if you're lucky just a bit of crippling, infection-prone torture-mutilation and a fine (that you may or may not be able to pay and thus risk very literal debt slavery).
The past wasn't just another country, it was another, vastly different world in so many ways.
If I had a time machine, I think i'd rather not even touch the world of 536 (or any such distant time) with a 10-meter cattle prod unless I could visit armed with an easily concealable and robust assortment of essential modern medications, and some powerful but compact concealed carry weapons.
Worth remembering too, the plague of Justinian was one of the earlier arrivals of Yersinia Pestis, and modern humans are at best only very marginally less susceptible to dying horribly from it than they were back then. You would absolutely need antibiotics with you at least. This is not to even mention something like the smallpox that widely circulated at the time. Who alive today who isn't in their 70s still gets vaccinated against the pox?