If I make a change in civedit, where do I put the bic file so that the changes take affect in the next game? Anywhere in the Civ3 folder?

There are two ways you can do this.
The easy way or the hard way.
The easy way just applies your rules to the games you start with those rules, and if you edit the rules after there will be no change in the game.
The had way involvs that, if you don't know what you are doing, you might end up reinstalling the game, and will affect current games as well. Might even mke them unplayable

The easy way:
Save it in the scenarios folder, and select load scenario instaed of new game when you want to use it. Then select your big.

The hard way:
Backup civ3mod.bic in your Civ3 directory, and save your mod with that name.