business aircraft depreciation

you can take 179 on the entire cost, but there can be limitations. your business need to have net income before the deduction at least equal to the cost any excess is a carryover. there may also be a limitation depending on its cost.  or you can take 100% (of cost as)bonus/special depreciation

read iRS PUB 946 chapters 2 and 3 

https://www.irs.gov/pub/irs-pdf/p946.pdf 

Yes if you elect to treat it as Section 179 property in 2022.  The IRS defines Section 179 Property as:

Section 179 property is property that you acquire by purchase for use in the active conduct of your trade or business, and is one of the following.

• Qualified section 179 real property. For more information, see Special rules for qualified section 179 real property, later.
• Tangible personal property, including cellular telephones, similar telecommunications equipment, and air conditioning or heating units (for example, portable air conditioners or heaters). Also, tangible personal property may include certain property used mainly to furnish lodging or in connection with the furnishing of lodging (except as provided in section 50(b)(2)).
• Other tangible property (except buildings and their structural components) used as:
  • An integral part of manufacturing, production, or extraction, or of furnishing transportation, communications, electricity, gas, water, or sewage disposal services;
  • A research facility used in connection with any of the activities in (1) above; or
  • A facility used in connection with any of the activities in (1) above for the bulk storage of fungible commodities.
• Single-purpose agricultural (livestock) or horticultural structures.
• Storage facilities (except buildings and their structural components) used in connection with distributing petroleum or any primary product of petroleum.
• Off-the-shelf computer software.

Since your business is flight training, the plane is used in the "active conduct of your trade or business" and is "tangible personal property" the aircraft will qualify for the full deduction.  

As Mike 9241 posted, the Section 179 deduction is not allowed in excess of your net income before the deduction so may be limited and create a carryover to be applied in future years.

@hankwin 

how is this affected by bonus depreciation. If bonus depreciation exceeds income, can it be carried forward

Bonus depreciation is not limited by net income in 2022 so it will create a loss.  The loss will offset any other earned income you may have outside of the business.  If your loss is in excess of your earned income, it will create a carryover like the Section 179 deduction.  You can either take the Section 179 deduction or bonus depreciation.

@hankwin 

So once an aircraft is fully depreciated, can I cost basis shift by putting it to work in a different company with a related owner?

Once an asset is fully depreciated, it has a cost basis of $0.00.  I'm not sure what you mean by "cost basis shift".  If you transferred an asset (airplane) from one business to another, the implications would depend upon what type of business each one was and the ownership of each business.  Additional information and a clarification of your question is necessary in order to provide an answer.