The single supplements depends entirely on the individual cruise line policies. Unfortunately most of those policies aren't good news for singles cruisers.
As for a cabin share, I know the TAs often get queries from solo passengers who'd like to join one of our groups. It might be possible to find a "roomy" that way. Also, if there's one you're considering, post a message on the message boards, because we do have quite a number of singles on the message boards, and it wouldn't surprise me if you could find a "roomy".