Sheila = girlfriend, minge = pussy, and "Bummer" sounds like "bum her" which means fucking her in the ass.

I'm not australian, or even native English speaker, but I think the joke is that he thinks he's suggesting to try Anal Sex.

I'm not Australian but I'm pretty sure this is the translation.

• Man calls help line because he was out with his girlfriend and she was stung by a bee on her vagina. He mentions that her pussy is completely closed up due to swelling from the sting. The help desk employee replies with "bummer mate" which you're supposed to think means something along the lines of "that sucks bro". But in an unexpected twist, the man replies with "Thanks mate, I hadn't thought of that". Which insinuates that he will have anal (BUMmer) sex with his girlfriend since her vagina is inaccessible.