I'd guess the plane is legally owned and registered by a Bermudan company that Trump owns, or he doesn't actually own the jet and it's leased from a Bermudan firm. Either way, the plane would run a Bermudan registry.
I've seen Trump's plane at LGA
several times, but never noticed the registry. Usually I notice that sort of thing - first time I ever flew on Air South, the Irish registration was the first thing I noticed...
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Photo © John Kelley
Most of "Bubbaflot"'s planes had Irish registrations, IIRC.