I find this sentence a bit odd.
There is an idiomatic expression "at spise som en fugl"/"to eat like a bird" which surprisingly means that you eat a lot, but it originates from the fact that a bird can eat its own body weight in food each day.
Unfortunately many people don't know the original meaning of the expression, they now use it to mean that someone eats almost nothing at all.
But i have never heard the expression to eat like a bear before. Maybe someone mixed it up with bjørnetjeneste