I wonder how long you could hide a cow transformation for? How long would it take before no matter what you did, everyone could tell that you were nothing but a big dumb cow?
It wouldn't be very hard to hide horns with your hair, you could put a tail down your pants leg if you had enough control over it, ears could be hidden under a hat or a hood, most people would never notice any of those.
What about when your face turns into a muzzle? a mask could hide it at the start, but eventually your face would get too long for the mask to cover all of it, and when your speech is nearly incomprehensible as you try to push out phonemes that your bovine mouth simply isn't meant to make, people will know that something is wrong. To say nothing of when your vocal cords change, and everything you try to say comes out as moos.
When your back legs change you probably wouldn't have much time left to seem human. At first you would look like someone with slightly odd posture, but when shoes stop fitting your hooves and your legs show through even the baggiest pants, nothing you can do will make you look like a person.
Your front legs (or "arms" as they'd be called in a human) would be even more damning. When your fingers start to turn hard and inflexible, you might be able to cover them with gloves, and find a way to keep your movements looking natural, but when all you have are two cloven hooves there's nothing you can do to give people even the slightest bit of doubt about what you are.
Maybe you'd be able to hide all of it for a while. Maybe your limbs would be the last to change, your muzzle still short enough to hide behind a mask, but your udder would give you away.
From the moment it grows in it would be almost impossible to hide how sensitive it was, how every movement lit up your nerves like a bonfire. Your quiet moans and the way your crotch jiggled with every step would leave no room for you to slip under the radar.
When the milk starts to leak out and soak through your clothes, and you can't keep your strange hoof-fingers in your pockets because you can't stop yourself from touching that pink mass, and it gets so big that your pants strain against it and the teats are so clearly outlined against the fabric, you'll know that nobody will ever see you as anything but a milk-filled dairy cow.
But you'll probably be too horny to care.