All theories attempt to explain known observations and make testable predictions.
I am not sure what 'truth' is in this regard.
The Big Bang hypothesis fits many of the known observed properties of the universe (red shifts, background radiation, etc.). It's not perfect, and may need alteration. I am unsure as to what the 'bouncing theory' is. Care to point to a peer-reviewed summary?
I would say the big bounce theory is more consistent with observations because in part the observation that the gravitational collapse of high entropy interstellar gas causes the initiation of nuclear reactions in stars that releases energy causes its expansion. Additionally the fact that the gravitational collapse of a star can cause it to supernova, and expand violently supports the conclusion the gravitational collapsed of the entire universe can result in a “Big Bang” or its violent expansion.
While there is strong theoretical reasoning to suggest that universe must enter a contraction phase based on the law of conservation of energy/mass because it tells us that the kinetic energy of the universe’s energy/mass cannot exceed its gravitational contractive properties. However because some of the kinetic energy of its components is not directed towards its expansion the total gravitational contractive properties of its energy/mass must exceed the kinetic energy of its expansive components. Therefore, at some point in time the gravitation contractive potential of its energy/mass must exceed the kinetic energy of its expansion because as just mentioned not all of its kinetic energy is directed towards its expansion. Therefore at that point, in time the universe will have to enter a contractive phase.
Please for a more detailed explanation of these ideas please visit our articles "Entropy and the Big Crunch" http://www.theimagineershome.com/blog/?p=5355 and the return of the big bang "The Return of the Big Bang" http://www.theimagineershome.com/blog/?p=34