Excellent question that clearly picks up on the symbolism of the river and what it represents to Montag at this stage of the narrative! You might want to consider how the river is described and in particular how Montag reacts to it. Note what happens when he first comes to the river:
He touched it, just to be sure it was real. He waded in and stripped in darkness to the skin, splashing his arms, legs, and head with raw liquor; drank it and snuffed some up his nose... Then, holding the suitcase, he walked out in the river until there was no bottom and he was swept away in the dark.
Note how Montag here literally bathes in the water and covers himself in it. Of course this is to overtly disguise his scent, but the ending of being swept away in the "dark" also seems to suggest that the river represents some kind of re-birth for Montag - he has left his old life, and is beginning a new kind of "birth."
Consider this paragraph:
He floated on his back when the valise filled and sank; the river was mild and leisurely, going away from the people who ate shadows for breakfast and steam for lunch and vapours for supper. The river was very real; it held him comfortably and gave him the time at last, the leisure, to consider this month, this year, and a lifetime of years. He listened to his heart slow. His thoughts stopped rushing with his blood.
This symbolism of the river as re-birth is extended here as the river allows Montag the space and time to reflect. He is described as if he were a baby in amniotic fluid, being "held... comfortably". His heart slows and he is able to think and relax. Clearly, therefore, the river symbolises the new start that Montag will have now he has escaped, and his new life with the rebels.
Hm, well, consider this:
When does Montag jump in the river? He's running away from the city, he's running away from the last bits of his old life as a fireman and as a part of that broken society, right?
Now, consider this, when we are all in the womb, we float around in fluid, right? As fetuses? And when we're born, we come out wet.
Usually when a character submerges him or herself in water it is a symbol if rebirth. Start there...