[Tyler Soares]" How do I convert my 4-3 footage so that it has the bars on the side, but still matches the sequence settings?"
I'm going to recommend against this, if you don't mind.
For sheer ease, FCP will upscale your video on the fly (Yes, you'll end up having to render it, but this should work quickly and easily.) The upscaling algorithm is decent, and there is a way to get it to better (at a longer render) via a sequence setting.
If you want to do this in compressor, I'd suggest blowing it up via the Geometry tab of the Inspector (in compressor). If you go to the dimensions of 1440x1080 with *square pixels* this should generate a 4x3 ProRes video. When it hits the background in FCP, there'll be black bars where there is no data (4x3 on a 16x9 frame.)
But to do exactly what you want, go to the Geometry Tab, set the Dimensions - frame size to 1920x1080 and set the Output (padding) to Preserve source Aspect ratio.
I have a couple of other concerns, YMMV (your mileage may vary) but there are three solutions, with the last one being the one you asked for. Test them all and see what you like the best!