could be the service, could be the server (waiter or waitress)

It depends what is meant by "Bedienung" in the context.
"Waiting staff" is the collective term for waitresses and waiters, including head waiters, maître d' etc.

It could also mean the service, as mentioned in #1.

Note that we don't usually refer to waiting staff as "servers".

@Mary

In the US, we sometimes do. For instance, after you're seated in a restaurant, a wait-person will come your table and say something like, "Hi, I'm Kelly and I'll be your server this evening." (I think it's an attempt to be gender-inclusive.)

Correction:

come to your table

Really, Eleanor? Is that a recent development then?

@Judith: Welche Art der Bedienung meinst Du? Personen oder Dienstleistung? Hast Du einen Zusammenhang (Kontext)? Dann bitte den ganzen Satz/Absatz hereinkopieren.

Normally it would simply be waitress or waiter.

an unfriendly way of calling for service in a restaurant would be just to shout "Bedienung!" in order to attract the attention of the waiting staff.

"Bedienung" in a restaurant usually refers to the waiter/waitress (i.e. the staff, not the service)

@penguin: As in a shop or supermarket, "Bedienung" in a restaurant does refer to the service (which is, of course, provided by staff as any service). For example:

Dort gehe ich nicht mehr hin, weil die Bedienung so unfreundlich ist.

This statement does not refer to a particular person, but to the way guests are treated by any waiter.

@Bastian: Da verstehe ich aber "die Bedienung" als Kurzwort für "das Bedienungspersonal", während "service" doch eher die von diesem erbrachte (oder eben nicht zufriedenstellend erbrachte) Dienstleistung ist.

Bastian, although I know disagreeing with you is futile, let's just agree to differ (see Dragon's post #9)