And there is no need to ask bishop about it.
Huh? I have no idea about Greek or Polish practices but in Finland we (EOs) are encouraged to get a sort of recommendation letter from our bishops if we want to commune in some other EO church. I would say that if we need a letter from our bishop to commune in an another EO church even more so we need one if we want to commune in an OO church.
That's what say Polish Orthodox priests I know. But the practice of the Finnish Church is very surprising for me. There is an official Eucharistic unity among all EO so why are you asked to get a recommendation letter from you bishops?
I understand the fact you should ask you priest if you can go to Communion in another EO Church e.g without confession prior to it or generally, if you're allowed to commune but it's nothing to do with communion in other jurisdictions, but with your practice regarding the Mysteries.
Last May when I was in Serbia in one of monasteries there was a Finnish Orthodox pilgrimage and they communed there. Of course I don't know if they had a blessing of a Finnish bishop, but I always though that's the most obvious expression of the Orthodox Unity: partake the Holy Eucharist in whatever jurisdiction you want, because we have the same faith, although a bit various traditions.
In Poland I know OO commune n Polish Orthodox churches and even one of Orthodox chapels in Warsaw is used by Copts and the blessing is given by our Metropolitan.
And some Orthodox use RC/Lutheran/other temples for services and it has a blessing of the metropolitan too.
Yes, I know, ever you parish used to use a Polish Catholic chapel. But I think with Coptc the situation is a bit different, becasue I suppose they use the same altar