Get one more transformer and build two of these, one for the negative and one for the positive.
The switcher circuits below require a very few components, no hot hot linear LM317 Oh My God It Burnt My Finger problems.
However, if you are in a linear mood, one schematic below is for a zero-volt min output LM317 linear approach, but the LM2678 type circuits are the more modern switcher approach, so much more efficient, runs cool, few parts.