It was already discussed in the comments that a water rocket needs to push "something" out. It is instructive to do the calculation in a little more detail to see where the "energy" goes. For this I will consider the relative share of energy going to the rocket and the "expelled matter" (gas, or water) as a function of the expelled mass. To simplify things, we will assume that all matter is expelled as a single entity with a certain velocity; in reality you might need to integrate, but any inequality that holds for a small amount of expelled matter will hold for the integral over many such amounts.
I will use upper case symbols for quantities relating to the "rest of the" rocket (mass M, velocity V, momentum P - without the expelled mass) and lower case for the expelled matter(m, v, p). From conservation of momentum, $P = -p$ so $M\cdot V = - m\cdot v$. The energy of the rocket $E_r$ and expelled mass $E_m$ will be respectively:
$$E_{r} = \frac12 M V^2 = \frac{P^2}{2M}\\
E_m = \frac12 m v^2 = \frac{p^2}{2m} = \frac{P^2}{2m}$$
It follows that the ratio of (energy in rocket)/(energy in expelled matter) is
$$\frac{E_r}{E_m} = \frac{m}{M}$$
In other words - the lower the mass of the expelled matter, the greater the relative amount of energy it contains. In the limit of "no water", the little bit of air mass contains virtually all the energy.
The river will not always follow the along the path of least resistance because as water flows, its momentum increases. If a river follows a bend/curve in the land, it may slosh against the bank or even go over the bank--but eventually, it will lose some of its momentum & then flow to a lower elevation or seep through the earth to a lower elevation. So as you can see the direction & momentum of water movement depends on other factors.
Best Answer
The gulping you describe is due to air being sucked into the bottle and temporarily halting the flow through the nozzle. When the bottle is filled with water, it is at a particular pressure. When you turn it over and some water leaves, the pressure is now lower in the bottle.
Once the pressure in the bottle is lower than atmospheric pressure, air forces it's way back into the bottle. This equalizes the pressure and water flows again. Then the pressure drops, air gets sucked in, and so on. Eventually all the water is gone and the bottle is filled with air at the same pressure as the atmosphere.