Who gets enters-the-battlefield abilities with Bribery?
When your opponent puts your creature into play with Bribery, it acts just as if they played it themselves (or, perhaps, put it into play from their own library). It's their creature, and the fact that you happen to own the physical card itself doesn't matter, except for some effects that explicitly use the word "own" or "owner". Terastodon does not have any of those effects. So it's your opponent who gets to choose what permanents to target and whether to destroy them.

If Terastodon dies, though, it will come back to your graveyard, not your opponent's. Once a card leaves the battlefield, then it does matter who owns the actual card.