This movie did something that movies do all the time: If the audience can't see it in frame, we have to do assume the characters can't sense it at all. Which is just silly. They never take into account smells, breathing sounds, footsteps, weight, or other ways to sense a person in the room with you. There might even be a high-pitched whine like a camera flash or computer monitor makes.
Also, nobody ever has any trust for the main character. Is it unreasonable when she says her dead ex, who everyone knew was a pioneer in high-tech optical technology, might have invented a way to be invisible, that SOMEONE might be using? Especially after his will was so cryptic and threatening.
Plus, the Invisible Man wouldn't be able to travel with her. There are parts of the movie where he'd have to either be in the car with her, or drive himself to follow her.