I sometimes think fondly of the lively discussion engendered by my post on “can’t be arsed,” especially concerning the way the way the expression has sometimes been (mis)heard by Americans as “can’t be asked.”
In researching that post, I encountered “can’t be bothered” as an expression meaning roughly the same thing, that is, being unwilling to do something because it would take too much effort or you are too lazy. The Macmillan Dictionary identifies it as “British informal” and gives these examples: “
“I said I’d go out with them tonight, but I can’t be bothered.”
“She couldn’t even be bothered to say hello.”
Google Books Ngram Viewer confirms the British predominance:
The ascending blue line post-1990 suggests NOOB status. Another piece of data is a 2005 song by country music’s Miranda Lambert:
And just a few weeks ago, this headline, referring to an obnoxious corporate executive who kept a list of employees who he felt were not up to the task, appeared in the New York Times:
Now all that said, I don’t believe Americans have as yet picked up on a related expression, “I’m not bothered,” meaning I don’t care one way or another. (“Would you like to go to a Chinese restaurant or a gastropub?” “I’m not bothered.”) Much less inverted and pronounced with th-fronting, a la the comedian Catherine Tate’s catchphrase:
notoneoffbritishisms.com 
Hi, Ben, your clip of the stupendous Catherine Tate might confuse people: from lip-reading it is clear she is saying her catchphrase ‘Look at my face’, which was then always followed by ‘Am I bovvered?’. Th-fronting: a regrettable trend that is making Cockney English obligatory over here.
https://images.app.goo.gl/YByZ1vbHdF2YL3Gd7
The clip in question is even further from that subtitle. It’s from her sketch with David Tennant as the Scottish teacher of double English, and she’s mocking his reverence of Shakespeare. She’s saying, “Look at my face. Is this a bovv’red face thou seest before thee?”
“Is one bothered?”
This is an expression that has two-fold meaning in our mixed-Brit/American family. All of us know and use it, as it is one of the permanent British fixtures in our linguistic life. However, it is also the expression I frequently pre-empt by saying things like, “This is not a ‘I can’t be bothered’ request; this is something I am asking you to follow through on.” Or, more frequently, “And please don’t tell me you can’t be bothered.” I am a pain that way (and other ways).
“I’m not bothered”–never heard in the USA.
I like a Gershwin tune how about you? It seems not in Ben and Jerry’s case as they are not familiar with the brothers’ 1937 song I can’t Be Bothered Now from the film A Damsel in Distress. Nor can they be Ella fans as she recorded it in her Gershwin Songbook Album. Doesn’t there have to be an element of newness for a word or expression to deserve Ben’s ire?
But that song is using the phrase literally, as in “don’t interrupt or trouble me”.
Bad news, go away,
Call round some day
In March or May —
I can’t be bothered now.
My bonds and shares
May fall downstairs,
Who cares, who cares?
I’m dancing and I can’t be bothered now.