Learn Dutch: Ja, bedankt!

Both mean 'thanks' or 'thank you'. Bedankt is a general word that works in almost any situation, whether formal or informal. Dank je specifically includes the informal word for 'you' (je), so it is best kept for casual situations.

Does bedankt change depending on who I am talking to?

No, it stays exactly the same! Because it doesn't contain a specific pronoun for 'you' (like je or u), you can use bedankt when speaking to one person, a whole group, a close friend, or a stranger.

Would I say Ja, bedankt! when someone offers me something, like a drink?

You can, but it is much more common for Dutch speakers to say Ja, graag! (Yes, please!) when accepting an offer. You would typically use Ja, bedankt! the moment the person actually hands the drink to you, or when confirming something you are grateful for.