They love the flower heads of larger Neoregelias for some odd reason. Sprinkling the ground around your broms liberally with cayenne pepper often does the trick. Repeat after it gets wet. Very cheap and humane, although often times a 12 gauge would be my choice.

I've had the same problem in my own garden in the past. The only thing I've found that worked long term, is to drape bird netting over the bromeliads, and pin the edges down with metal pins that are used for securing 1/2" poly drip tubing. I know that a lot of people would find the aesthetics a bit objectionable, but after I while, I stop seeing the black netting, as it is almost invisible. It works, and I can say the same for the cayenne pepper or ammonia or any other foul smelling solution; it just seemed to rile them up to destroy more plants.

Get some of the bobcat or cougar scent ...it will run them off for good

Possums love pineapples so I wrap mine with chicken wire.