It is a known fact that water and electricity should not be used at the same time but have you ever wondered why? Were you ever told that you could be electrocuted while showering or bathing, during an electric storm? Can an electric current really flow through water?
In order to answer these questions, another must be asked: does the water contain an electrolyte? In order for electricity to flow there must be ions in the water. Electrolytes are species that produce ions in water.
All compounds can be categorized into three areas: strong electrolytes (exist almost 100% as ions in water), weak electrolytes (less than 100% production of ions) and non-electrolytes (produces no ions). Only strong and weak electrolytes are of importance for this discussion.
Conductivity, the measurement of the flow of electricity, depends on both the identity (strong, weak or non) and on the concentration of the solution.
Weak and strong electrolytes mainly come from two sources: acids and “salts” or ionic solids. Each donates ions into the solution very differently.

Acids

Acids are actually covalently bonded molecules that do not contain ions. They are only able to produce ions in water because of the transfer of a hydrogen or “proton” from the acid to the water. This produces the hydronium ion (H₃O⁺) and a negatively charged base (A^–).
There are six acids, called the strong acids, that will ionize completely, or nearly so with water. All other acids are considered weak. Interestingly, water is considered a very weak acid. It does “self” ionize into a hydronium ion and a hydroxide ion, luckily very weakly though.

Ionic Solids

Ionic solids are already composed of ions that are held by electrostatic attraction (positives and negatives). Because of its polarity, water can dissociate or separate these ions by providing a counter attraction.
Two factors help determine whether an ionic solid is either a strong or weak electrolyte:

1. How strongly attracted are the ions in the solid/lattice to each other (lattice energy) and
2. How strongly are they attracted to the water (solvation energy)?

Concentration

In order to conduct electricity, there must be enough ions, regardless of their source, to allow movement of the current through the water.
Visualize the ions as stepping stones across a river. The more stepping stones there are, the closer together they become and the easier it is to travel across. Increasing the space between those stones makes crossing more difficult until they are so far apart that it becomes impossible. The same is true of ion concentration. Even strong electrolytes can become dilute enough to become non-conductive.
Let’s revisit the original question, are you at risk of being electrocuted in your bath during an electric storm?
Granted, water does naturally contain some ions, but not enough to carry a current so it all comes down to what is in your water. Electrolytes are everywhere! Even if you tried to bathe in deionized water, the salt from your skin, the soaps you wash with, even the hardness of your water create a wonderful electrolyte solution.
Once again it would ultimately come down to the concentration issue which is wonderfully explored in the Physical Chemistry textbook with various theories.  As for myself, some experiments aren’t worth the shocking experience of being wrong and I stick to the adage:  water and electricity don’t mix.