I haven't brought an air rifle from the USA, but generally it isn't too much issue.
In terms of the airline, check with them in advance as to their policy regarding transporting firearms (airguns will be treated as firearms in the eyes of the airline).
They are normally considered as sporting goods and may be eligible for a free baggage allowance.
An airline approved flight case will be required - the more durable it is the greater the likelihood of your gun surviving intact.
I don't know if you would experience any issue at the US end of things, but from a UK perspective, once your flight case has been recovered from the special baggage desk for you airline, you will need to go through the red channel to declare it - as long as it complies with current UK legislation there shouldn't be any problems.
Last time I came back to the UK with an air rifle, customs asked what it was. I told them air rifle compliant with 12ft.lbs limit - they had a quick look and I was on my way - quick and painless.