First of all, grass within a bunker (on a bunker face or within a bunker) is not part of a bunker in a Rules of Golf context and as of a recent Decision (in the last go-around) either is the "revetted" face of a bunker. It's considered to be "Through the Green".
However, in America anyway, where it seems that grass bunker faces and surrounds (the grass area around sand bunkers) are getting longer and more penal every year, it would do golfers well to recognize that they probably need to avoid bunker surrounds more diligently than they need to avoid the sand surfaces of bunkers (which are the only area designated as "bunker" in the Rules of Golf) for the simple reason grass bunker "surrounds" seem to have gotten so much more penal than the sand surfaces of bunkers.
I'm about to explain this to our membership in a report and something distinctly tells me they are not going to like to hear it.
I have no doubt they will quibble and fuss over this reality but just as the American general responded to the German general when asked to surrender with the single word "NUTS", my reply to the membership will be either the two word response "TOUGH COOKIES" or "EAT GRASS".