The bass could be shallow year round due to low dissolved oxygen deep, lack of habitat deep, maybe just preference; some bass stay shallow year-round regardless of temperature/weather.
My aeration timing recommendation depends on the type of aerator used. Diffused aeration systems (compressor that pushes air to a diffuser located at the pond bottom) aerate, but also, more importantly, circulate the water vertically near the diffuser. Diffusers can help keep the pond from stratifying, therefore reducing or eliminating the risk of turnovers, and they keep aerobic bacteria breaking down organic junk at the bottom of the pond which helps manage nutrient loads and slows siltation. You can make a reasonable case for running diffused aeration systems 24/7, 12 months of the year, but I think if you want to save electricity they can be turned off during winter. You absolutely should not initiate diffused aeration during the hottest parts of summer, because it WILL cause a turnover that could result in fish kill. You may also notice a denser algae bloom, murkier water for weeks to months after starting a diffused aerator from increased nutrient circulation and plankton growth; this is less likely in a newer pond or those with less organic accumulation on the bottom.
Surface aerators, like vertical pumps, fountains, paddlewheels, are very good at aeration but do little to no circulation. I usually only recommend these in shallower ponds (diffused aeration becomes less efficient in less than about 6-8 feet). Since these only aerate the surface, and do not disturb stratification, I only recommend running these during the warm months (roughly March/April-September/October) only at night, or 24 hours during turnovers and after 2 or more days of solid cloudy weather. It's a waste of electricity/wear to run them during the day because aquatic plants and algae will produce enough oxygen to saturate the surface (the same level the aerator would be aerating) on warm sunny days.
Some considerations on solar powered aeration. Unless there is a battery storage option for the aerator to continue operating at night or during periods of heavy cloudy weather, I don't think solar aeration does much good. The periods when aeration is needed most, at night and during dark cloudy weather, are the same periods a traditional solar powered aerator would shut off. Same goes of wind-powered aerators. Just something to consider.
If there are updates to solar aerator tech, hopefully some of the other forum experts will straighten me out.
Here are some of the companies I'm aware of that offer surface, diffused aeration, and solar powered options:
https://airolator.com/ MO
https://easypro.com/ MI
https://kascomarine.com/ WI
https://www.nashvillepond.com/ TN
https://www.outdoorwatersolutions.com/ AR
http://thepondboss.net/ FL
https://www.scottaerator.com/ MI
Most, if not all, of the pond management companies in the state sell and install aerators too.