I think that the only thing you'd need to copy to either application directory or mingw/bin is SDL.dll. The following process worked for me after with SDL 1.2.15 development libraries. My CB might be a bit old (build 7289), but I doubt it would make a difference:

1. Set sdl variable BEFORE creating an SDL project. For me it crashes CB entirely or just did funny business in earlier versions.
To set sdl variable go to Settings->Global Variables, click New that's on the same line with Current Variable. Name it sdl. Set base to the directory where you unpacked the SDL package.
2. Create new SDL project with default values.
3. Build = if it works - great! If it doesn't then check under Project Options->Search Directories->Compiler and rename $(#sdl.include)\SDL to $(#sdl.include). Try again.

I think that the only thing you'd need to copy to either application directory or mingw/bin is SDL.dll. The following process worked for me although my CB might be a bit old (build 7289):

1. Set sdl variable BEFORE creating an SDL project. For me it crashes CB entirely or just did funny business in earlier versions.
To set sdl variable go to Settings->Global Variables, click New that's on the same line with Current Variable. Name it sdl. Set base to where you unpacked the SDL package.
2. Create new SDL project with default values.
3. Build = if it works - great! If it doesn't then check under Project Options->Search Directories->Compiler and rename $(#sdl.include)\SDL to $(#sdl.include). Try again.