How can I speed up the ADC?

Other Hardware Sensors
2

Why do you feel you need to speed up the ADC?
Isn't getting on for 10000 conversions a second fast enough? (That's one conversion every 2/10th of a mm)

Now, it's just a simple black line so I don't need 10 bits of accuracy.

If it is a simple black line, why do you need any more than one bit?

Edit:
Is the problem that you're not doing anything else during the 100 or so microseconds needed for a ADC reading (i.e, the processor is busy-waiting for a result)?
This is easily addressed.