How do you know a reaction is not occurring when you mix the two solids? The only cue we have that a reaction occurs in the solution state is the formation of bubbles of escaping carbon dioxide. If there is no liquid to displace, would we be able to tell if carbon dioxide was being produced? Yes, but not with the naked eye.
The real issue is that the solid state reaction is much, much slower.
To produce carbon dioxide, the bicarbonate ion needs to come in contact with an acidic proton on citric acid. This is unlikely in the solid state since there is very little kinetic energy.
In solution, there is more kinetic energy, so the molecules are more likely to encounter each other. Additionally, the proton transfer can propagate quickly through the hydrogen bond network in water.
$$\ce{HCO3- \bond{...} H-OH\bond{...}H-OH\bond{...}H-OH\bond{...}H-OH\bond{...}H-Cit}$$