would a bathroom without a gfci outlet be a violation in a rented appartment
If you failed an inspection they must tell you why. 

As Alt asked above, do you not have a receptacle at all, or is there one there but not GFI protected? 

Under codes going back to the 70's bathroom receptacles must be GFI protected. Before that there was no GFI protection so an earlier installation could very well  have a non-GFI protected receptacle and still be 100% code legal, as long as no renovations have been done to the bathroom.

On to your question, again, if you failed there must be a reason for it. What kind of "inspection" was it? I don't know what Section 8 is, but if it's some sort of assistance program they tend to have some very strict rules and can make landlords do a lot of things a private rental would not have to do. 
So in summary, you may very well have to install a GFI protected receptacle to be part of this program.