Can “noch einmal, bitte” be also used to ask someone to repeat an action (ie in a bar to get another bottle of beer) ?

Or should I use “noch eine Flasche Bier, bitte” ?

Couldn’t you say “noch einmal das Gleiche, bitte” to the waitress if you want another beer? That doesn’t sound that strange to me.
But again it would be a thing you asking for not an action. If you want to say “Can you (please) do it again” would that be “Kannst Du es (bitte) noch einmal machen?” / “Können Sie es (bitte) noch einmal machen” Or using tun for machen even though that seems to be strange in a formal sentence.
Or specify the action. Like “can you (please) say it again” would be “Kannst Du es (bitte) noch einmal sagen” or if you want to listen to something again( like the new germanpod101 lesson ) and ask “Can you please play that again” that would be “Kannst Du es bitte noch einmal abspielen”
But I think to get another beer you aslo could rais your bottle and say “noch eines bitte” (another one please)

“Wie bitte?” is perfect for asking someone to repeat something. It’s polite, especially compared to “Was?” or “Häh?” - these expressions are what first comes to mind, but children are taught not to say them because they are rude.