"The rest of us are fairly mortified at jokes made at the bloke's expense."
Would you please explain what "bloke's" expense means?
It a joke is made at someone's expense, it means that the joke makes fun of that person, makes that person look foolish, etc.
In this case, "someone" is "the bloke", which refers to a male person who is not further identified in the context given.
bloke is a British English term.
The American equivalent is 'guy'.