Exactly. If you own 11-20 champions, get two self-bans. If you have 10 or fewer champions, you get one self-ban. 21-30, three self-bans, etc. So every week, look at the champions you own and those in free rotation, decide which you would least-like to play, and then self-ban those champions.
Just to clarify, this would not impact pre-game trading. Like, if for some reason you wanted to trade with the guy who had Singed (like, if he was a buddy that you knew would do a lot better with the champion you got, for example), that trade option would still show up. The self-bans only influence what random champion you receive initially, and what you receive from rerolls.
I had originally considered just giving everyone a number of self-bans = to 10% of the total number of champions, (I think there are 138 champions now, so like 14 self-bans) with the idea that they would set their bans once and then not have to worry about it. But, with ARAM-only accounts, people could use all those bans to cancel out most of the free rotation every week, guaranteeing that they end up with good champions of their choice in ARAM. Since the point of this system is to avoid the champions you really don't like (in your case, Singed), rather than help people end up with only a few specific champions, having the total number of self-bans be based on the number of champions the player owns seemed more reasonable.