What I would like to either find or develop myself is the appropriate code to open a bitmap file on the SD card (keeping in mind that the basic access to the SD card FAT filesystem with the SD library is already working)
The SD card and the SD library, specifically the open() method, do not care that the file is a bitmap file. Or an excel spread sheet. Its a collection of bytes. That the collection means something to some application is just a happy coincidence.
and to parse the bitmap file
Have you google reading bitmap files? They are quite well organized (strange for a Microsoft invention, I know).
generate a single array corresponding to a single line of the image
You'll need to be a lot more specific about the type, size, and contents of that array.
write that line out to the LED strip
You said, or at least implied, that you knew how to to that. At least for some type/size/contents of an array.