Get random double (floating point) value from random byte array between 0 and 1 in C#?

Assume I have an array of bytes which are truly random (e.g. captured from an entropy source).

byte[] myTrulyRandomBytes = MyEntropyHardwareEngine.GetBytes(8);

Now, I want to get a random double precision floating point value, but between the values of 0 and positive 1 (like the Random.NextDouble() function performs).

Simply passing an array of 8 random bytes into BitConverter.ToDouble() can yield strange results, but most importantly, the results will almost never be less than 1.

I am fine with bit-manipulation, but the formatting of floating point numbers has always been mysterious to me. I tried many combinations of bits to apply randomness to and always ended up finding the numbers were either just over 1, always VERY close to 0, or very large.

Can someone explain which bits should be made random in a double in order to make it random within the range 0 and 1?