Mandy actually really likes Billy as crazy as that sounds. She even got super possesive of him when his de-aged mom tried to steal him away from her.
The real reason why is mainly shown through the movie. Mandy's biggest fear is not just her becoming a fat mice lady married to Erwin. Her biggest fear is actually that life has gotten so boring that she does turn into a fat nice lady who is regularly rescued by the big black man (which also happened earlier in the movie). In short, she doesn't want her life to be boring or be the damsel in distress who always rescued.
With Billy, she gets chaos, adventure, and the chance to be the one who rescues people (namely Billy and sometimes Grimm).
Tldr; Being with Billy is never Boring.