Do members of the Eastern Orthodox church have their own holy book besides the Bible?

or do they read an Orthodox version of the Bible?

They read an Orthodox version of the Holy Bible.

The Bible we use is the exact same, with the exception of the Old Testament - which is translated from the Septuagint (Greek) and not the Hebrew. This version contains the books supposedly missing (Tobit, etc).

Chryseraphim gave exactly the right answer.

"Holy Book"... no.

HOWEVER

There are some other writings that are held in high regard.
These include the writings of "The Desert Fathers" (early monastics who lived in Egypt before the 7Th century,) "The Holy Fathers" (other saints and monastics throughout the ages.)

While the Bible is the primary resource and the standard used to judge the validity of all spiritual writings, other writings are used for personal insight and edification. If we read what some of the great minds wrote, it is not necessary to re-invent the wheel every generation.