No, you have to buy induvidual bottles for each colour, but it works out like this:
Okay, So the price for a bottle of ink is $8.00, and lets say you bought your copic for $5.25, which is what I sell my markers for on my website. You can refill your copic up to 10 times before you run out of ink in that bottle, so that $8.00 bottle is the equivalent of spending $55 dollars on markers! They're very much worth it in the long run of things.
But honestly, you probably wont have to refill that much either. I refill a marker around four times a year, so that bottle of ink will last around 2 1/2 years.