Wouldn't Leia cease to be a princess?

The world she was the Princess of was destroyed... Why did people continue to refer to her as "the Princess"?

As an honourific that she deserved the title.

Besides, whilst Alderanians still exist (and obviously not all were on Alderaan), she can still be Princess.

Except Bail was a Senator? Don't recall him ever being called King

As the year went by perhaps he started taking after the Emperor, and made his own little Empire at Alderaan?

He wouldn't have to be a King, just royal. But as Leia was a Princess his royal status reasonably follows.

Hmm, may it be that whatever peoples title is at home that they are called Senator when representing their world in the Senate?

May Bail be a King at Alderaan but be called Senator because he is the representative for Alderaan?

Kinda like Dragonball Z Prince Vegeta still sayians around therefore still a prince of his people, wasn't cos padme was a former queen?

If Bail is the King of an entire planet what's he doing galavanting over the galaxy to Senate meetings, surely they have at least one extra diplomat on an entire planet

Perhaps he only was a Prince. And that his father was the King and died sometime between RotS and ANH.

^I'd say that's probably the case.

Bail was married to the Queen of Alderaan.

Why do we still call the US Presidents, President? Ie President Clinton, President Carter, etc.

The same reason retired Generals and Admirals (and pretty much every military rank) are still referred to as "General" by other military personnel. They earned the title, whether through promotion or vote in the Presidents' cases. For a time, they were the most powerful men in the world. They get some kudos for that. They still get Secret Service too.

As for Leia, her mother was Queen of Naboo too, so really she's a double princess...

No, that title is elected- Padme wasn't a Queen at the point she had Leia.

60,000 inhabitants of Alderaan survived the Death Star's laser, being off the planet at the time.