You can make an LM317 go to 0v even without a negative transformer. The trick is to add two diodes between GND and the (-) output of the PSU (so, your outpur is aprox 1.4v above the real GND). The diodes must be able to handle the max output current and the power dissipation. The resistive divider that controls the LM317 output voltage is also referenced to this point.
You will need to consider the power dissipation of the LM317 in the worst-case scenario and use a suitable heatsink. The datasheet has a very good explanation on how to calculate this under the "Heatsink Requirements" section.
EDIT: i'm sorry, the circuit i posted before won't work, it was just a part of a circuit i did which had a current limit that could go all the way down to 0v, but for the CV control to go down to 0v, you need some way of getting 1.25v below your main diode bridge's negative output. I should have checked the circuit carefully, instead of sketching it and posting.
Anyways, if you use the LM317, remember to check the "Heatsink Requirements" section, and forget about using a 48v transformer. The power dissipation for the chip is about (input_voltage - output_voltage) * current. Try to use a transformer/bridge/capacitor combination that will result on a voltage that just goes over the requirements for the LM317 for the output voltage you need (check the dropout voltage), and whatever additional drop that the final circuit could introduce.