Due to changes in the way Photobucket does business, a link to an adventure doesn't work. I have the link, but get a 502 error if I try it directly. I have the game ID, is there any way I can get to the game without using the broken link?

If it's a game here, game URIs are generally of the form textadventures.co.uk/games/view/(id)/(name).
So just put in the ID and you can find it.

Not sure what photobucket has to do with anything, though.

To add to mrangel's input:

If you linked directly to the game (to play, not to the game's main page), it will be like this:

http://play2.textadventures.co.uk/Play.aspx?id=[your-game-id]

It used to start with play.textadventures.co.uk rather than play2.textadventures.co.uk, but that was changed a couple (or a few) months ago. (It was back in July.)

That could be the problem, too.