Power adapter versus Power supply
Here's what's going on.

The LM317 is what is known as a linear regulator. You are going from 18 volts to 6 volts. To do that with a linear regulator, the 12 volt difference is converted into heat. The regulator is trying to dissipate that, but it can't, so it's getting hot and going into thermal shutdown. 

My guess is that the bench power supply is running a lower voltage than the laptop power supply

You have a few options. 

You could reduce the input voltage to the regulator, to something like 9 volts. That would reduce the dissipation drastically, though it might not be enough. Note that linear regulators have what is called the "dropout voltage", which is a delta between the input and output voltage. The datasheet says it's about 3 volts, so 9 volts would be about the minimum.

You could add a heat-sink to the regulator; that would allow it to dissipate more heat. It would still get hot, but it would let the heat get away more easily. 

You could use a different kind of power supply - known as a switch power supply (in this case, running in "buck" mode) that can convert from 18V to 6V at a much higher efficiency. They are relatively cheap.

Or, you could find a 6V power supply / adapter that will give you the current that you need. That would be the simplest to do.