You are correct, but Bodhisattva (just like an Ahrat) is not a fully enlightened being. He has not yet overcome the final delusion of Nirvana. His compassion is noble, but it’s based on a relationship, and in its core his compassion is fundamentally still suffering. He is not yet completely alone.

When Bodhisattva overcomes his compassion he becomes a Buddha. A Buddha does not reside in either Nirvana nor Samsara - he doesn’t see a difference. Both Bodhisattva and Buddha can teach, but a Buddha doesn’t feel compelled to.

So, to answer your question (in Buddhist terms), Bodhisattva ends his cyclic existence when he becomes a Buddha.

There’s a notion, popularized by Allan Watts, that Bodhisattvas and Ahrats (or “solitary Buddhas” as he called them) are two types of Buddhas, two “destinations” so to speak. This notion is incorrect. They both know the Buddha, but they are separated from the Buddha by the final duality between Nirvana and Samsara - they are just on the different sides of it. Bodhisattva wants people to join him in Nirvana, and Ahrats are enjoying their Nirvana by themselves. So they both see people as suffering, they just take a different view as to what to do about it. They both need to realize that there is no difference between Nirvana and Samsara and plunge into complete aloneness.