Short Answer: It depends on the acceleration with which it is thrown downwards.

Explanation:The bubbles rise up due to the force of buoyancy which comes into play in fluids due to the increase in pressure as we go deeper into the fluid. The pressure, as we go a height h into the fluid is given by:

P=P(atmosphere) + hdG

Here,

P(atmosphere) is pressure due to the atmosphere which, on Earth, is equal to 10^5 Pascal.

h is the depth at which we are observing the pressure.

And G is theEFFECTIVEacceleration due to gravity.

Now if a is the vertical component of the acceleration vector,

G(effective) = g(vector) - a(vector)

g, as you must be knowing, is the acceleration due to gravity having a magnitude 9.8 m/s2 directed vertically downwards.

Thus the net buoyancy force, which is due to the pressure difference depends on G which in turn depends on the vertical acceleration you have given the fluid contained in the bottle.

Now, note this, since we are talking about vectors here, the downwards vertical is considered positive here, so,

If, a > g AND directed downwards,the bubbles will, wait for it, MOVE DOWNWARDS!

and if, a=g, as another guy already mentioned (:/) the bubbles will be motionless.

and if, a<g, the bubbles will move upwards as usual.