He knew that his employers had ordered it. He let Steve kill him. It was part of Bishop's philosophical fatalism - he accepts (and in a way welcomes) the inevitability of his own death. He's tired of his job and tired of living. Death doesn't frighten him at all.
Yes. I said on another thread that he pretty much exhibits a kind of "death wish". He'd like to exit his profession, but he doesn't really see a way of doing it successfully. Then Steve arrives on the scene.

Bing.duke
gets
it.
Whose idea was it for the word "Lisp" to have an "S" in it?

He dies. The rumours of there being an alternate ending (with Bronson's character surviving) are simply an urban myth. Director Michael Winner always corrected this widely believed untruth when people asked him about it. Winner insisted that he only ever shot one ending, and that's the ending we have.
The point is that Arthur Bishop knew he was going to die. He knew that his employers had ordered it. He let Steve kill him. It was part of Bishop's philosophical fatalism - he accepts (and in a way
welcomes
) the inevitability of his own death. He's tired of his job and tired of living. Death doesn't frighten him at all.
He rigged Steve's death before they left for Europe, knowing that Steve would kill him as soon as the '
assignment
' was over. Bishop accepts his own death, but also rids the world of a sadistic degenerate psychopath (which is essentially what Steve is) by posthumously terminating his former apprentice. Poetic justice.