In most of the other Slavic languages it's the same, "do" means "until." "Hasta la vista" is a direct translation of ES, "until the seeing" (literally), meaning good-bye. RU: До свидания ("do swidanija"), UA: До побачення ("do pobaczennia"), BY: Да пабачэння ("da pabaczennia"), CZ: Na shledanou, SK: Dovidenia ("dowidienia"), BA/HR: Doviđenja ("dowidzienia"), RS: Довиђења ("dowidzienia"), SI: Nasvidenje, MK: Довидување ("dowiduwanie"), BG: Довиждане ("dowiźdane").
"Do" is just a part of "Do widzenia" = "Goodbye" (literally it means more or less "until the next time we see us" (like the Spanish "hasta la vista"; note that "do widzenia" is formal)).
"Po" and "do" are both prepositions and I don't think it is easy to give a rule when to use which (for example http://sjp.pwn.pl/szukaj/po.html lists 19 situations in which you would use "po") or how they translate to English. Some examples:
"Chodzę do szkoły" = "I go to school"
"Poczekaj do jutra" = "Wait until tomorrow" (like in "do jutra" or "do widzenia")
"Zapisz się do chóru" = "Sing up for choir""
"Jest po północy" = "It is after midnight"
"Jestem po drugiej stronie ulicy" = "I am on the other side of the road"
"Spaceruję po lesie" = "I am walking in the woods"
"Poszedł po chleb" = "He went to buy bread"
It seems as if you use it right before supplying more information to a particular part of a sentence? Like the first example on your link translates to 'The echo spread through the forest', using 'po' before it specifed 'the forest.' no.12- 'Butelka po mleku' uses 'po' before specifying that the bottle is for milk. in your example above, he went to buy bread, use 'po' before specifying it was bread he bought ect? I dunno, but many of the examples seem to fit that general idea, probably just a shot in the dark and po may be just the Polish equivalent of the definition of 'round'.
I would say that 'po' is about spreading over the something. And 'do' we use to specify a direction to something. So, the echo is spreading over the forest, you go for bread and you are 'spreading' over your way (it's more about purpose of your walk not the direction). But if you say 'see you again' then you leave a gap before that moment. And you specify the exact direction to it: "Do widzenia", "do szkoły", "do jutra", "do chóru". Does it make sense to you?