If you need to reverse the polarity, the common approach is to use a H-bridge. You can either find them all integrated, or implement them with discrete transistors. If the integrated option is too expensive, use cheap MOSFETs (you'll need 4 per segment - a lot to put on a circuit, but can still be pretty cheap.)
If it's acceptable to first toggle off all segments before changing the full digit, you may be able to find a trick to reduce the number of required transistors.