I'm not familiar with Gimp, but what you're describing is very likely a filtering artifact, as Falconius said. For more information on filtering, read this thread: [Award Winner] Bitmapped Images - The technical side of things explained. Posts 9-13 are the most relevant to this topic.
In a nutshell, though, if there is a filtering, anti-aliasing, resampling, or interpolation option (all four of those terms are roughly equivalent), you need to set it to either "nearest neighbor" or "none." It may be in the tool itself, or it may be a global setting. That will ensure that the software does not create any intermediate colors when transforming. Instead, it will pick the color of a pixel based on whatever whole pixel in the original shape that fell closest to it after the transform. Be aware that if your lines are less than three pixels wide, nearest neighbor filtering may create holes in the line after a rotation. That could interfere with your ability to bucket fill.
Based on the description of your workflow, though, I wonder if you might be more comfortable with vector software like Inkscape? Vector objects are not groups of pixels, but are actual shapes that you can manipulate to your heart's content without ever needing to worry about pixelization or filtering. It may take a little bit of time to learn the new tool, but you might find it better matches the way you want to work.