I just watched a Mythbusters episode about this.
Yes you can die from dropping certain electronics into your bathtub.
Bathroom appliances (hair dryer, curling iron, etc) made after the 50's or 60's are equipped with a safety switch that clicks when it hits water and will not work. If you can source a 1950 hair dryer it WILL work.
However appliances with heating elements worked astoundingly. For example, a toaster that's plugged in and actively heating up. Very high level of electrocution far beyond what is required for death.
The episode also details additional factors that increase success, such as how far to drop the device in from the tub drain, and test things like how the presence of bubble bath, urine, etc impact results.