This depends on many factors such as: the solubility of air in the solution, the distance from air inlet to the surface, the temperature and pressure of the solution ... etc. So, I think it is better to have some experimental work to be done to investigate the expected bubbles behaviour.

The question has wide possible cases to answer. Increasing or decreasing depends on the size of the bubble you are talking about. The reduction in volume of the bubble is negligible when the bubble volume is 2 orders of magnitude (100 times) greater than the reduction in volume and you can say there was no reduction in volume. The same cannot be true if the bubble size is less than 10 times the reduction in volume.

The reduction in volume is the most possible solution when the solution is not saturated, the volume of reduction is proportional to how low is the dissolved air in it already.

Increase in volume of the bubble also is possible in the case of over saturated solution i.e. highly aerated solutions. for eg. aerated cold drinks and beverages. 

For a given size of the bubble, given size of dissolved air in the solution and for a given height of the solution or residence time of the bubble in the solution, you can come up with an equation for the change in size of the air bubble. This would be more appropriate.

During aeration of solutions, how do the sizes of air bubbles change while they reach the surface of solution? Do they increase or decrease?

Do you mean: how does the size of one air bubble change during the rise from bottom to surface? Or do you consider a swarm (normal aeration). How are the bubbles generated and what is their initial size? Which height is considered? What kind of solution?

Bubble size will increase (when rising) due to hydrodynamic pressure decrease. Bubble size may decrease because of oxygen mass transfer out of the bubble (but water may evaporate into the bubble; possibly other compounds especially carbon dioxide in bioprocesses may transfer into the bubble). When considering swarms breakup and coalescence will occur depending on initial bubble size, power input and solution characteristics and so influence bubble size.

So more information is needed to give a more relevant answer.

And, as mr Sallam indicates, for calculations, solubility, pressure and temperature are needed. And mr Rajeshwaran indicates you should consider whether the change is relevant in your case. And, indeed, a model (equation) is possible, but not always simple e.g. when also other compounds are involved.

Regards