Can you activate a loyalty ability of a planeswalker that was put onto the battlefield under your control with Bribery?

When Bribery resolves, you search your opponent's library and put a creature card onto the battlefield under your control. However, if the card you find happens to be a planeswalker (note: planeswalkers are not creatures unless something makes them so, so this is a moot point for Bribery specifically — but the general principle applies to any effect that puts a planeswalker under your control).

For any effect that does put a planeswalker onto the battlefield under your control, CR 606.3 states that a player may activate a loyalty ability of a planeswalker they control only at sorcery speed, only once per turn, and only if no loyalty ability of that permanent has been activated that turn. Ownership is irrelevant — control is what matters (CR 108.4).

So if you somehow control a planeswalker — regardless of who owns it — you are the one who activates its loyalty abilities on your turn. The loyalty ability costs (adding or removing loyalty counters) function normally under CR 606.3.

Concrete example: Your opponent uses Bribery against you and takes your Liliana of the Veil. On their next turn, they control Liliana, so they can activate her +1 or −2 loyalty ability once during their main phase, just as if it were their own card. You no longer can, because you no longer control her.

In short, loyalty abilities are governed by who controls the planeswalker (CR 606.3, CR 108.4), making stolen or borrowed planeswalkers fully usable by the new controller.