"The bit depth" may relate to how much values a boolean can take. In most languages, it can take two values: true or false. In object oriented languages, if a boolean is an object (like Boolean in Java), the value can also be null (and some languages, apart from null, support a state called uninitialized, which can mean any value).
The size of the boolean in memory is an entirely different question. As already mentioned, for Java it is undefined, and if I recall correctly, it will likely depend on the WORD size of the system the program runs on. Theoretically, a boolean can be one bit in size, but only when we need many booleans, we can use that (called flags variables), because we are bound to the WORD boundaries of any system.
The size in the compiled image can be different again (in the event of constants), but you normally shouldn't need to worry about that.