I'm northern. There's no r in beer
Bet I'm more northern than you and I say beerrrrr! 
My beautiful, clever, favourite Aunt was a Beatrice (and at 6ft tall known as Big B!) I absolutely love the name and over the moon it's back in fashion.
We would say Beet -riss (as uneducated weegies!) but a far more elegant way to say it would be Bay - ah - triss