It is not safe to hide in a bathtub during an earthquake. You should drop to the ground and take cover by getting under a sturdy table or other furniture.
According to Ready.gov, here's what you can do during an earthquake:
If you are inside a building:
Drop down onto your hands and knees so the earthquake doesn’t knock you down. Drop to the ground (before the earthquake drops you!)
Cover your head and neck with your arms to protect yourself from falling debris.
If you are in danger from falling objects, and you can move safely, crawl for additional cover under a sturdy desk or table.
If no sturdy shelter is nearby, crawl away from windows, next to an interior wall.Stay away from glass, windows, outside doors and walls, and anything that could fall, such as light fixtures or furniture.
Hold on to any sturdy covering so you can move with it until the shaking stops.
Stay where you are until the shaking stops. Do not run outside. Do not get in a doorway as this does not provide protection from falling or flying objects, and you may not be able to remain standing.
If getting safely to the floor to take cover won’t be possible:
If getting safely to the floor will be difficult, actions before an earthquake to secure or remove items that can fall or become projectiles should be a priority to create spaces..
Identify an away from windows and objects that could fall on you. The Earthquake Country Alliance advises getting as low as possible to the floor. People who use wheelchairs or other mobility devices should lock their wheels, bend over, and remain seated until the shaking stops. Protect your head and neck with your arms, a pillow, a book, or whatever is available.
If you are in bed when you feel the shaking:
If you are in bed: Stay there and Cover your head and neck with a pillow. At night, hazards and debris are difficult to see and avoid; attempts to move in the dark result in more injuries than remaining in bed.
If you are outside when you feel the shaking:
If you are outdoors when the shaking starts, move away from buildings, streetlights, and utility wires. Once in the open, “Drop, Cover, and Hold On.” Stay there until the shaking stops.
If you are in a moving vehicle when you feel the shaking:
It is difficult to control a vehicle during the shaking. If you are in a moving vehicle, stop as quickly and safely as possible and stay in the vehicle. Avoid stopping near or under buildings, trees, overpasses, and utility wires. Proceed cautiously once the earthquake has stopped. Avoid roads, bridges, or ramps that the earthquake may have damaged.
Find motr Earthquake Safety Tips, Preparation, and Readiness at National Geographic.